I am trying to change the anchor point on my head with the anchor tool. I have anchor open in transformations. I am getting strange results due to this triangle of anchor points (see attached). How can I fix this? I did try to parent at one point, but am unsure of how to unparent. Thank you in advance.
If you tell us about a problem with the Anchor Point and don't show us the Anchor Point, we can't help you. I see that everything is normal with your points because we do not know what you are doing. You should make a recording of your screen while doing what are supposedly the "strange results" in order to have a clearer idea and try to see where the issue is.
Uploaded screenshots are difficult to see and annoying to deal with. Please embed your screenshots using the toolbar. Cropped screenshots are pretty useless when it comes to diagnosing problems. We should be looking at the entire UI with the modified properties of the problem layer revealed. That's also a good way to diagnose a problem. Select the layer with the head (if the screenshots were not cropped I would know what layer that is), press 'uu', and take a look. You should see at least 5 keyframes for Position because the position because Position keyframes and position motion paths are the only paths that will show up in the Composition Panel. Only in the layer panel can you choose to render other motion paths.
If you have position animation and you then change the anchor point using the anchor point tool (y), the position of the layer before and after the anchor point change will be different. If you have also set anchor point keyframes then the head is probably in the right position somewhere in the timeline. That's where you should start.
If you still cannot figure out the solution to your problem pose a full UI screenshot showing all of the modified properties of the layer and describe exactly what it is that is happening and what you want to happen in the timeline. We can probably help you out.