(CNN) -- Leisha Hailey and her girlfriend Camila Grey would like to make one thing clear: They were not making out on the Southwest flight the pair say they were booted from.
The couple released a statement through their band, Uh Huh Her, to clarify the incident, which happened on Monday.
"In no way were our actions on Southwest Airlines excessive, inappropriate or vulgar," the statement said. "We want to make it clear we were not making out or creating any kind of spectacle of ourselves, it was one, modest kiss. We are responsible adult women who walk through the world with dignity."
Hailey, an actress from the Showtime Sapphic drama "The L Word," tweeted Monday that she and Grey "have been discriminated against by @SouthwestAir. Flt. attendant said that it was a 'family' airline and kissing was not ok."
Hailey called for her followers to boycott the airline and demanded an apology.
"We were escorted off the plane for getting upset about the issue," she further tweeted. "@SouthwestAir endorses homophobic employees. No one made her accountable."
Southwest Airlines posted a statement Monday on their site, saying that "Initial reports indicate that we received several passenger complaints characterizing the behavior as excessive. Our crew, responsible for the comfort of all Customers on board, approached the passengers based solely on behavior and not gender. The conversation escalated to a level that was better resolved on the ground, as opposed to in flight."
Southwest adds in a statement to CNN Tuesday that "Additional reports from our Employees and Customers onboard flight 2274 during a stop in El Paso on Sunday now confirm profane language was being used loudly by two passengers. At least one family who was offended by the loud profanity moved to another area of the cabin."
The statement continues, "Although we have reports of what Customers characterize as an excessive public display of affection, ultimately their aggressive reaction led to their removal from the aircraft. We do not tolerate discrimination against anyone for any reason. In this situation, their removal was directly and solely related to the escalated conversation that developed onboard the aircraft."
Southwest goes on to say that their "tenets of inclusion and celebration of diversity among our Customers and Employees — including those in the LGBT communities — anchor our Culture of mutual respect and following the Golden Rule...ALL are valued and welcome." According to the statement, the airline has reached out to the couple to offer a full refund.
This incident is the latest for Southwest, which last year landed in the news after filmmaker Kevin Smith was asked to leave a plane when officials told him he was too large to occupy a single seat. Earlier this month, Green Day lead singer Billie Joe Armstrong was kicked off a Southwest flight for wearing saggy pants.
Hailey and Grey said in their statement that they were in the process of filing a formal complaint with the airline and that "We hope that when all is said and done a greater tolerance without prejudice will evolve."