Use a finger nail buffer (NOT a nail file) from Superdrug or similar. Work slowly and, ideally, only on surfaces not visible on the wrist, of course.

Try to work 'flat (buffer) to flat (on the lug)', except on the inner/lower lug edge, where you have to 'break' the edge to remove the damage.

Whatever you do, don't make things worse.

If the watch was expensive, take it to a good local jeweller. I've used two: a one man band and Pragnell, both of whom were happy to do the work for no/little (£30) money.

Why people buy a watch they value and then bu@@er the lugs is one of watch-keeping's great mysteries.

It does explain the name 'bugger-lugs', though.