Removing Grease Nipple

Looks like it's a one that's tapped/ pressed in. Put the nut back onto the thread and lever off with a flat head screwdriver or a small cold chisel

Use a vice grips. Squeeze it tight at the butt of the nipple and twist it off. Have you freed the ball bearing at the top of the nipple and seen if you can grease it after that.

Usually the nipple is threaded. And it should twist off. However it looks very rounded.

What usually blocks them is a bit of hard grease below the ball.

You have a better chance trying to twist out than trying to pull out. The twisting action might loosen it.

Even a cigarette lighter to heat it a little would help.

If your determined to remove it use a slide hammer.

drill it out and put a new one in.

You should be able to heat it until red hot - that should allow for sufficient expansion in the threaded part to allow the nipple to pop out.

I wouldn't drill either as it might just start spinning in the hole.

I would be more inclined to cut it off with an angle grinder and see what I would do then have you tried taking the housing holding the nipple off. That looks like a bearing at the bottom with a treaded compression ring holding it in place. See if that will twist off