Excuse my ignorance - once I've polished the area (T-cut? Similar?) Then do I need to seal it afterwards?
I use Meguiars #205 finishing compound for minimum cut. I would be a bit unsure about using t-cut as I would not be confident at how much that would remove and the finish it would leave, would it need a finer compound afterwards? Sealent wise, yes, you will need to re-seal it, is your car ceramic coated or waxed?
@MrJollygood; T-Cut is almost an expletive to detailing enthusiasts!

I would avoid using old school T-Cut as it’s quite an aggressive product and as @Watts has said, you run the risk of removing too much clear coat and striking through to the colour coat - especially if you inadvertently apply too much pressure. With any paintwork correction, the general rule is to start off with the least aggressive product to minimise removing more clear coat than is necessary, and if a low cut polish doesn’t achieve the desired effect, then move on to a polishing product with a higher degree of ‘cut’. The danger is that you may end up buying lots of different products and you still don’t end up with a result you’re happy with.
If you’re able to give approximate details of where you’re located, there maybe a forum member near to you who’s into detailing and has a DA polisher and a range of polishing compounds who may be able to polish out the etching - or at least improve it. Alternatively, any professional detailer local to you should be able to polish out the etching - shouldn’t be too expensive if they’re only doing spot correction and it might work out cheaper than buying lots of products and not being entirely happy with the results through hand polishing. Bear in mind that whatever method you decide to use (polish by hand, machine polishing, professional detailer), if the etching to the clear coat is particularly severe, then it might not be possible to correct it entirely.
If you do attempt to hand polish the etching out, a product such as Farecla Scratch X might work - it was used by hand to remove bird poo etching in this old discussion thread at the link below;
https://meguiarsonline.com/forums/showthread.php?1535-Scratch-X-to-remove-bird-droppingsAs @Watts has said, you would need to reapply whatever wax / sealant product you’re using to provide protection, as a polishing product designed to correct scratches or etching in paintwork will remove any existing protective layer.
Another option is the heat method - using a heat source such as a hairdryer or heat gun on the etching. I’ve not tried this so can’t vouch for how successful it is or what the risk is of permanent damage to the paintwork if the heat source is too hot, held too close or applied for too long. It seems to work in this YouTube video, and I’ve seen it discussed as a successful method on detailing forums;
https://www.youtube.com/watch?v=hCaXNUSiud8Good luck - I hope you get it sorted to your satisfaction

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