Paint Question

Not a normal question here - but here it is. I have recently noticed pale, white circular stains on my hood. No idea what it is but have tried cleaner wax, soap and water, and a clay bar. None have taken it out. It has a composite clear coat (not factory but repainted where the clear coat is mixed into the paint). Could try polishing compound but am hesitant. I know it is a difficult question to answer, without seeing the damage, but any ideas???? Bobby