They simply are keyframes. Delete the keyframes and set the remaining ones to Bezier. Alternatively, since you know how to do this already, you can copy& paste masks and keyframes as paths into AI and optimize them there, then copy&paste back. Just make sure the clipboard settings are set to AICB.
If you are using the Paint tools those options don't exist in After Effects. The only work around is to set a keyframe for the brush path, copy the keyframe, then go to Illustrator and in a blank document the same size as your layer paste. Once in Illustrator you can simplify the path, select it, copy it, then go back to After Effects and select the same keyframe then paste. If you get a mask instead of a new path delete the mask path, make sure you have only the original brush path keyframe selected, then go to Edit>Paste from the menu.
It doesn't look like you're drawing a mask path. That might be a better way to go.
You're not copying the path keyframe. You're copying the effect keyframe.
Open up the timeline like I said above and find the brush path. There will not be a keyframe. Set one, then copy it and paste it into illustrator. Don't copy the keyframe that's already there.