I remember catching her frequent appearances in the early 2000s and thinking this was someone special – a very young woman doing a subtle kind of humour at a fairly advanced level. David Letterman, with assistant Stephanie Birkitt, talks to Mario Andretti before the start of the 2007 Indianapolis 500. Credit:Getty Images Part of her appeal was that she was just so different from what we saw on TV then. The reigning comic actresses of the day – acerbic Tina Fey and Amy Poehler, bubbly Jennifer Aniston and Sarah Jessica Parker – were balls of fire, performers with a capital P. But Birkitt was a little awkward. OK, very awkward. She fidgeted. She slouched. She didn't exactly sell her lines with verve. But that was the point. In Letterman's self-aware talk show-about-a-talk show – with cameos by the petulant cue-card guy (Tony Mendez, also sadly written out of Late Show history) and jokes about failed jokes – Birkitt wasn't an actress playing a smart-aleck page mouthing off to the boss. She was playing "Dave's assistant," recruited on the cheap to come out and pretend she was a smart-aleck page.

She didn't really seem to care if you believed it. And that's why it was funny. This image rendered from video shows David Letterman, speaking on the Late Show in 2009 days after revealing on air that he'd been sexually involved with women from his television program, apologises to his wife saying she had been 'horribly hurt by my behavior.' Credit:AP At the time, I assumed Birkitt was an ironist by profession, a bright young comedy writer or underground sketch performer with a knack for conveying the gawkiness of the college babysitter. A talent we would see more of soon. It's hard to believe, but she's 40 now. Even as their affair turned into a public disaster in 2009, when her producer boyfriend attempted to extort the talk-show host, she was already 34, a law school grad who had just passed the bar – solidly a member of Generation X. Actress Julia Roberts in 2001 with host David Letterman. Credit:Reuters

But Birkitt's shtick foreshadowed a kind of comedy that we now associate with millennials. Think of Greta Gerwig, Lena Dunham, the broads of Broad City – actresses whose brilliance is the ability to convey a very naturalistic and youthful self-consciousness. They give the impression that they just wandered off the street and onto the set to play their slacker selves. It looks easy and spontaneous, but it's a gift. And that was Birkitt's thing. Part of me keeps waiting for Stephanie to surface in a story arc on Girls, maybe as Ray's klutzy new barista girlfriend. Stephanie Birkitt: her boyfriend tried to extort the talk-show host. But the bigger part of her appeal, of course, was her chemistry with Letterman. It was glorious to watch them. None of these exchanges I'm typing up for you are particularly funny to read – you really had to see them. He clearly took as much delight in her appearances as a drop-in from Julia Roberts or Tom Hanks. But Birkitt was no movie star, and their dynamic was one you could relate to: It was great office chemistry, like the fun table in the employee break room, trading inside jokes with your favourite cubicle-mates.

This ordinary young woman was cracking up this titan of comedy, and letting us in on the joke – and it made the edgy, aloof Letterman seem relaxed and fun. Knowing what we know now changes everything, of course. They were wildly, inappropriately, in love with each other. That's what the on-screen magic was all about – the arm punching, the pet names ("Vicki," "Smitty," "Monty"), the eye rolling, the mouthing-off to the boss. It's difficult to re-watch some of their scenes together. Like the time he cajoled her into demonstrating her ex-boyfriend's dance moves for the audience, heaving her torso around to the riff from Rod Stewart's Da Ya Think I'm Sexy? He's not mock-ogling her, we realise now. He's ogling her, and she knows it and he knows she knows. Of course it's difficult to re-watch any of their scenes together, and that's because you can't. Her presence seems to have been wiped clean from the vast CBS catalogue of YouTube-accessible Letterman clips. It's even tricky to find bootleg clips of her nearly 300 Late Show appearances; the only ones that remain on the Internet are a few postage-stamp sized QuickTime videos that a dedicated superfan started collecting long before there was a YouTube, and a few others that are so unusably blurry they must not have been worth the copyright complaint.

It's a reminder that sex scandals are always harder on the women, tainting their career achievements if not outright erasing them. Unlike many of the women caught up in a scandal, Birkitt has never spoken publicly. She appears to be living in Los Angeles, a member of the California bar. "I appreciate it," she said when I called to tell her I was writing a tribute to her, "but I don't have any comment right now." What did Birkitt mean to the Late Show? At a time when Letterman was two decades into superstar status, she channelled something of the spirit of his exciting early days on the air, when viewers didn't know what to make of this giddy, goofy, occasionally hostile guy. Maybe she wasn't a great comedic talent in the end – maybe she really was the gawky assistant just being herself, rolling her eyes at the host for real, not as an act. Whatever it was, it definitely worked. Top Stephanie Birkitt moments on The Late Show:

Survivor "Did you see, or touch, any monkeys?" – Stephanie's recurring question to the Survivor cast members Letterman was obligated to host for a few years. Little Bo Peep "Stephanie, I notice you have a little outfit on. What is the little outfit?" "I'm Little Bo Peep."

"Little Bo Peep, Little Bo Peep, ladies and gentleman. [applause]. . . and why are you dressed as Little Bo Peep?" "Because you made me." – Stephanie presenting the CBS Mailbag in a 2003 appearance preserved here by a superfan. Mrs Carney "Ha ha ha ha ha! Good one Mr Carney! You're hilarious! Ha ha ha ha ha! Oh, Mr Carney, you crack me up with that toupee!" – Stephanie to Dave in a 2005 appearance, a shtick that started months earlier with him occasionally calling her "Mrs Carney." Of course we didn't piece it together at the time.

Jackass "You know, Mr Carney, this is the part of the show where we do our little skit about some nonsense, and then I call you a 'jackass' and then leave?" "That's right, yes." "Well, I forgot to write up a little skit." "Ohhhh, more's the pity, Vicki!"

"Yeah, so I thought people would really enjoy getting a look at my new rolling backpack." "Uh, you know, Vicki, I really don't think we have time to ..." "Here's where I put my things. It's light as a feather. It has the wheels right here ... " "Good, uh huh, that's nice ..." "Jackass! [Waves] Good night everybody!"

– Stephanie and Dave in a 2005 appearance.