I don’t print TPU on a textured bed. I use the flat side of my build plate, which I also have coated with a giant sheet of Kapton/polyamide tape. Peeling the completed parts off of the smooth surface has never been an issue.

A word to the wise: Always run with a sheet of polyamide tape if you have a flat build plate. This will go a long way towards protecting the finish and flatness of your plate, and I have definitely saved myself a couple of times when having a Z offset that was too low and thusly crashing the nozzle only into the tape and not the surface of the expensive plate itself. You can apply adhesive and clean the tape’s surface just the same as the PEI surface of your plate, but once it gets worn out or chewed up or otherwise no longer produces parts with a pretty underside, you can just peel it off and reapply. If you’ve already fucked up the surface on your plate you can also paper over this with a layer of tape which will smooth out small scratches, pock marks, and other imperfections.

And if you really need to employ the nuclear option to get a stuck part off of your bed (i.e. if you’ve printed something with a sticky filament such as TPU or PETG and happened to have your Z offset way too low) you can peel the tape off along with the part. The tape is unlikely to survive this process, but a pack of 12 sheets is only $20 or so.