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Rachel Lindsay must know it's just a matter of time before the world loses interest in her season of "The Bachelorette" ... so she's milking the spotlight.

Rachel and her new fiance, Bryan Abasolo, were swarmed by paps Tuesday as they arrived at the BUILD studio in NYC ... and they took their sweet time to suck face for the cameras.

In her defense, Rachel's season finale was Monday night -- so it makes sense she'd be making the rounds, posing at all the stops along the way.

Still, this display of affection is a bit too on the nose for us not to cringe. Congrats, though ... here's hoping they're couple #6 to actually tie the knot for 'Bachelor' Nation.