Yeah, that's something Moho just does. I think it has to do with how it interpolates the smoothness of the curve as it passes through the points. I don't think you can completely get rid of the bumps, but you can probably minimize them with a few adjustments.
For example, I would try fattening up the point that's currently set to 50%, and moving it a little closer to the 100% point. Like so...
Tip: I personally avoid making the end point on a stroke 0%...I like to give the point a slight roundness as in the above example. I think this looks a little more 'natural' and less 'digital'. In your example, I see you need the next curve segment to be invisible, but instead of going 0%, try using the Hide Edge tool on that segment instead.
Bezier handles might also let you work with how far the width falls off from the point. I'm skeptical that this will be better, maybe just different. Also, Bezier points might not animate as you would expect. It's worth a try but be sure to save a copy of your project first.
An alternative approach is to draw the line as a filled shape, which will give you the exact shape you want, but this does complicate the shape for animation. I don't recommend this except for special cases (like, maybe for an extreme close up on the eye.)
Hope this helps.