United Airlines has apologized to a female passenger and given her a $500 travel voucher after she accused the company of giving away her first-class seat to a Texas congresswoman, an airline spokesperson said Monday.

Jean-Marie Simon, 63, of Washington, DC, claimed she was tossed aside to make way for Rep. Sheila Jackson Lee, a Houston Democrat, on a Dec. 18 flight.

Airline officials told reporters that their internal systems showed that she canceled her trip following a weather delay, but Simon denies doing this.

A United spokesperson said the company had offered Simon the apology and voucher in an attempt to make things right. But she claims this didn’t happen, either.

“United has not apologized to me,” Simon told The Post in an email early Tuesday. “A low ranking employee responding to an online customer complaint apologized on the phone, in his individual capacity. He also said he would send my complaint up the chain at United. To date, I have not heard from United.”

Furthermore, Simon claims she was actually given her voucher back on Dec. 18 — “when United cancelled [her] ticket.”

“This was far from an apology,” she said. “The gate agent who issued it told me to either ‘Take it and get on the plane or find another flight somewhere else.’”

Simon said a gate agent originally tried giving her a $300 voucher, which she refused.

“I’ve seen people get twice that for voluntarily giving up seat on overbooked flights,” Simon tweeted Sunday. “When I asked for free meal/bev., gate agent said, ‘And I want a Mercedes Benz, but I’m not going to get it.’ ”

Simon said she was only able to get her voucher and apology by “insisting.”

“United threatened to remove me from plane for taking photo,” she tweeted. “United manager called me @ home: said United behavior at gate/on plane contra [sic] United training. Said taking photos is legal, andaid [sic] United will investigate to c who did this to me.”

Simon had been on a flight from Houston to DC when she lost her seat last week. She had used 140,000 of her frequent flyer miles to purchase the ticket, along with another to Guatemala.

“It was just so completely humiliating,” Simon told the Houston Chronicle of the incident.

Jackson Lee, meanwhile, claims she did nothing wrong.

“I asked for nothing exceptional or out of the ordinary and received nothing exceptional or out of the ordinary,” she said in a statement this weekend. “But in the spirit of this season and out of the sincerity of my heart, if it is perceived that I had anything to do with this, I am kind enough to simply say sorry.”