Hi @yellowrobyn,
Many thanks for the additional images and details.
That exterior pictureappears to illustratea fairly standard look foraged linseed-based glazing putty. First, I believe it would be a good idea to determine if there areany water leaks. Is the timber inside the window spongy or rotted? I can see a little bit of deterioration, but thatcould just be the filler, and it doesn't necessarily reflect that there's a leak.
For instance, please take a look at the window putty used on the property I rent.
Someone very inexperienced has used glazing putty themselves and done a horrific job. Saying that, though, there are no leaks. The putty doesn't always need to look perfect to seal water out. If there are no leaks in your instance, you might be able to get a better look by skim coatingover it without having to redo the putty completely. This would be optimal, as I must say, glazing putty is not particularly pleasant to use. It's sticky and doesn't smooth out like a cement-based filler.
You might like to start by taking a flat head screwdriver and doing a bit of exploratory work on the inside of the window. Have a little dig around those areas hard up against the glass. If that is just putty and not rotted timber, then you'll be able to sand it back and just fill the area withEarl's MulTfill Ready To Use Filler - 0.140kg White.
If there are no signs of water damage to the interior, I would suggest possibly leaving the exterior alone. If you don't like the crinkled look, you could attempt to sand it smooth and then fill over it.
Let me know how you go.
Mitchell