Can UV-C sterilizers damage phone screen?

Cleaning products are not advised: Cleaning your iPhone - Apple Support.

Apple isn't going to respond here. We, you're fellow users can speculate but, unless someone drops in who's an engineer, I don't know that it would be more than that.

You can certainly contact Apple directly. Start with the Contact Support link in the upper right corner of every page.

Best of luck.

The usage information for the iPhone X OLED (and other models using LCD) repeats the advisory not to use any cleaning fluid on the phone. This also applies to all display products because of their oleophobic coating fused to the glass. We learnt this from the retina display #Staingate incident and recall. More recently, my iPhone X developed suddenly an unexplained smudge below the coating suffice and this is still pending apple's review.

I don't use anything except water on microfiber cloth to wipe phone display, but the apple store uses Whoosh. On my previous LCD iPhones and MacBook Pro, and iPad Pro, I have used the Fellowes screen cleaner. But generally, it's not recommended that any cleaning fluid or chemicals be used to clean or sterilise the display surface. I can't imagine how UV-C as a form of germicidal irradiation should be used on the phone but it should not affect the phone's coating which is fused to the glass. UV-C generally affects cell nuclei and hence effective as a germicide and may not do anything to the phone in that respect.

You might want to contact the developer of the product in question.