The check ball in the pump bonnet can be removed, however it isn't easy and I've never been certain it was designed to be removed. Patience and cleverness are the keys. The problem is in removing the retaining ring without destroying it, honestly speaking. It is a press fit in there and there are 4 tiny bumps which stop the travel once it is pushed back in. If you want to do this, I'd suggest getting a very small crochet hook or hooked type dental pick and working ever so carefully around the perimeter. There will be a post from one side to the other (diametrically). Alternatively you might use a toothpick with the sharp tips removed. Push down on the ball from the top and see if you can get any motion doing that. You might tap lightly on the toothpick to do that, also. The truth is the little piece holding that ball in place is thicker than you might expect, but it can be bent and damaged. I'd guess yours might be 1mm thick. Replacing it is easy, obviously. As for heat, probably not. I don't think that would help in this case.
As for the check ball, yours might not be a ball but a brass piece that looks much like the needle in the needle and seat (only smaller). Once again a dental pick (straight) or any sort of rigid thin rod (music wire or possibly even a paper clip straightened) might be enough to dislodge it. Once free it usually will fall out when you turn the body over. If yours has the weight and ball...same thing. You need to try to gently free the weight and the ball should follow. When they're stuck like this I clean them up using a common bamboo skewer or small dowel pin sharpened like a pencil or some other round piece of wood which can be made sharp on the end. Get some polishing paste (MAAS, Flitz or Semichrome), put a bit on the sharpened tip of your bamboo skewer and rotate it down inside the hole until you see the "seat" is nice and smooth. A jeweler's loupe is helpful here. I realize not everyone has one of those, but they're very handy. Get a cheap pair of sunglasses or better yet reading glasses, poke out the lenses and you can fit your loupe in there and secure it. I use mine on my left eye, but that's because in watchmaking I always left my dominant eye free to look around at a distance. Years ago I had one which was very solidly stuck. I poured a penetrating oil in the hole and left it for a couple of days and that helped. Think I used Liquid Wrench. I wouldn't waste my time with P T Barnum Blaster, but I understand some people like it...and it might work ok. It seems to me to be another over-marketed and under-engineered product. Kroil used to be good, but I've heard it has changed now. Good luck. Keep us posted.