Hi,
Depending on the screw size you could try using a screw extractor;
https://www.ebay.co.uk/itm/12pc-Dam...245268&hash=item2ac587d4e2:g:trkAAOSwrANcncME
The concern with removing these screws is to avoid collateral damage to the surrounding tiles so a lot of care needs to be exercised. It also depends on your experience using tools; breaking a drill bit in a screw will only make the job a lot worse.
I have excellent workshop facilities so I'd possibly drill the screw heads to completely remove the head this takes practice; then I'd use a short length of steel tube having filed teeth on the end of the tube the teeth arranged to cut in reverse; the bore of the tube to be slighter in excess of the screw gauge; chuck the new tube in a drill and run the drill slowly in reverse allowing the new tube to remove the plastic wall plug from around the remaining screw; repeat for each plug; the screw should then come away.
I seldom get away with doing things the easy way so I dream up more complicated ways of doing a job.
Using heat as suggested could possibly work by removing just enough plastic to gain a grip on the screw end but I'd be careful not to use too much heat in case the plastic then bonded to the screw?
Nail polish remover (acetone) could also be tried in order to melt the plastic but depending on what type of plastic the plugs are made of this might take quite a bit of time.
I've never used a Dremel but perhaps using a Dremel fitted with a small metal grinding wheel could possibly add a new screwdriver slot but not if the screws are very rusty.
Do you intend installing a new grab bar; if so would it be possible to drill new holes and add a plastic backing washer to cover the old screws under the grab bar mountings? I'd recommend using either brass or stainless screws?
Just Ideas.
Kind regards, Colin.