This is the first adaptation of a Richard Stark/Parker novel to use the character name Parker. Although the following movies are based on the "Parker" novels, the name was always changed: Point Blank (1967) (Walker), The Split (1968) (McClain), The Outfit (1973) (Macklin), Slayground (1983) (Stone) and Payback (1999) (Porter).
Parker calls his girlfriend and her phone displays a caller ID of (504) 723-2343, which, when Googled, is the phone number of a Louisiana film crew person with the last name of Parker (who doesn't appear to have worked on this movie).
While showing Parker a mansion in Palm Beach, Leslie inquires if he's married, and Parker tells her that his wife passed away. While Parker could be lying as part of his alias, this could be a reference to the first Parker novel "The Hunter" where Parker's wife commits suicide after he returns from being betrayed and left for dead by his wife and partner. "The Hunter" was previously adapted in John Boorman's Point Blank with Lee Marvin and Brian Helgeland's Payback with Mel Gibson.
When Parker is holding the chair to Hardwicke's brother's neck, he threatens to break his trachea. This is possibly a reference to one of Statham's previous movies, Safe (2012), where he breaks someone's trachea and says "I didn't know tracheas could break."