Do people replace Tag Heuer watch bezels?

Looks like people sell them here

Yep. You might also be able get a good jeweler to polish the scratches out which might work out cheaper. If the watch is older than 2 or 3 years it would be a very good idea to get the thing serviced particularly if you are going to get it wet as the O-rings can start to degrade and you lose water resistance. If it’s’ a mechanical mechanism (as opposed to quartz) a service will help to keep it running smoothly and keeping good time.

Getting Omega to do a full service on one of their watches, including all parts (except the crystal), costs around £125 (the last time I had it serviced which was a couple of years a go) and it came back looking like new. Tag Heur may offer a similar service.