The TiVo remote control doesn't officially support TCL televisions, sadly, but after some digging around on the Internet I found a suggestion to try out the RCA codes. The suggested code didn't work for my model, but the 0004 (RCA 1 of 2) did. This is to control Power, Volume, and Mute. I never did find a code for TV Input, but I only tried a dozen or so before giving up as that is less important to me.
More specifically, this is for the TCL Model LE39FHDE3010 39" LED TV.
Curiously, the user's guide says the following about programmable remote controls:
"This TV utilizes new remote control signals and may not be compatible with your existing universal remotes. (...) Over-time newer universal remotes and set-top boxes will become available that should pick up the new TV codes."
I have no idea what they're trying to convey with that statement, other than "rotsa ruck," but there is a lot of discussion out there about how finicky these TVs are to control with third-party remotes. If this is important to you then you should think twice about a TCL.