Thanks Tim! That add-in is exactly what I was looking for, without knowing what to look for. Worked perfectly to remove the point.
I really poorly worded my second question, and ended up figuring out the answer. With the LGIM disabled, by default there are relates on the lines layer between it and the points layer based on the ToPointID and FromPointID fields. With the LGIM enabled, these relates aren't established. It's handy if you want to identify a curve center point and, through the relate, see which curve/parcel it belongs to.