Domed caps or a couple of squash balls sound like the ideal low-maintenance solution, so will give those a try. Much appreciated for all the suggestions.
Here's a picture. Turns out it's pretty much exactly 1cm diameter and there are two spaced 16.5cm apart.
We don't want to go through the hassle of tracking down a new one that has the correct fitting and length, any extra nonsense fitting it, etc., so are just looking to smooth it all off...
I have recently moved into a new home and will cover renovations at a future date.
The current situation with the bath is that it's otherwise usable but the in-bath grab handle is broken and I have removed all plastic shards of handle.
However, the threads for the screw fixtures (one at each...