After some testing I've figured out what's up here. This, it seems is a consequence of importing paths from Illustrator.
(Seems to me it would be easier just to draw these simple paths right in After Effects to begin with – but anyhow)
Here I've got three examples:
The one on the left is straight from Illustrator (just as you've done)
The center one has been created within After Effects
The one on the right has been imported from Illustrator after I fixed it
Going through the layer stack we see that my first example displays the same little square at the top-left as yours does... while the others do not. We also see when we get to the 'Group 1' layer that there is an anchor point in the same location as the little square, while the others have their anchor points in their respective centers as they ought to:
Taking a peek at the Transform properties for the first path confirms that the anchor point is not at zero:
So how did this happen? Taking note of the numbers (22 and 247) I went back into Illustrator and put my detective hat on...
What seems to be happening is that when importing this way, the X and Y coordinates are transferred from the Transform Panel in AI to the anchor point in AE. Here is my Transform Panel in Illustrator:
So (if you must import paths this way) rather than mess around trying to fix it in After Effects, let's just fix it before it's exported from AI... The solution is simply to zero out the X and Y values, and then save. Here's what it looked like when I saved it:
The result then is the fuchsia path (on the right) which appears to be just the same as the version created within AE (except one is called 'Shape X' while the other is referred to as 'Group X').
The little square is no longer there and the anchor point is now centered as it should be.