Foxx's comments came during debate on a hate-crimes bill that bore the name of Shepard, who was brutally attacked in Wyoming and left hanging on a fence to die. Foxx said he was killed during a robbery, not because he was gay.
Judy Shepard was in the House gallery when Foxx made her comments.
In an interview with a Winston-Salem TV station, Foxx said she "simply chose a poor word."
According to today's Winston-Salem Journal, she said she sent a handwritten note to Shepard's mother. She told the station, "if I said anything that offended her, I certainly apologize for it and know that she's hurting, and I would never do anything to add to that."
The paper said the Matthew Shepard Foundation confirmed that Judy Shepard received Foxx's note, but declined to comment.
"We are not commenting any further on Rep. Foxx's remarks on the House floor, or anything that was contained in a letter," Logan Shepard, the foundation's communications associate, told the paper. "Everything that has been said already, is enough. We are trying to focus on the positive, which is, that the (hate-crimes bill) has been passed onto the Senate."