Any ideas how to remove this?

[Thistles24]

Hoping to find a cleaning/diy guru that might have the answer!
We got new interior doors for our house, some of which are glass panelled. My father very kindly offered to varnish them for us, but unfortunately left the plastic protective film on the glass as he did. I’ve removed what I can, but there’s LOADS of tatty bits round each frame. Tried soaking it, using tweezers to pull it, which got a bit more off but was scared of scratching the glass. Any other ideas? Took so long to save up to get the work done and now these tatty doors are all I see

Scalpel/craft knife

Get a surgical scalpel and when you're alone in the house and unlikely to be disturbed spend a bit of time cutting the tatty bits off. It takes a steady hand and you can't do it if there are pets or people leaping about, but it really does work.

Try a scraper for a ceramic hob. They’re a couple of quid online.

Have you tried scoring very close to the frame with a sharp Stanley blade?