I don't want to be a doom-monger but the missing paint from the rivet heads and cracked paint around the joint suggests to me that the rivets are fatiguing and will eventually fail, so touching up the paint is probably the least of your worries. Can you see movement in the bracket relative to the frame when you operate the derailleur? If so I'd suggest you stop using the bike until it's sorted as this could be damaging the frame.
Potentially a scary undertaking but I'd suggest that the best course of action might be to drill out the rivets, remove the mount, clean everything up, re-attach the mount with new rivets then touch it up (or paint the bracket a different colour entirely prior to fitting to avoid an obviously bad match).
What's the bike just out of interest? Looks like an early-ish one from the branding. Has it done a lot of miles? IMO rivets aren't an ideal way of mounting a fairly highly-stressed component; a conclusion also apparently reached by Boardman as well as my 2017 Team Carbon's bracket is bolted on (hopefully to some sturdy inserts integral to the frame!).