That’s a response damper.
Reposted from LeeDesign:
Basically, it acts as a “spacer” between the string loop and the response area to prevent snagging. It is a vital component in yoyo design, and can have tremendous effects on the response of the yoyo. There are two variables you can play with in the design: thickness of the lip, and the height of the protrusion. Thicker dampers will reduce the response but provides smoother play for old strings, while thinner dampers makes for better response with fresh strings but compromises smoothness for old strings.
Apparently it’s been around since the old YoYoJam o-ring design, but served a different function originally. It makes the groove’s inner wall deeper to secure the o-ring without the groove cutting too deep into the body. The unintended function of buffering the response was realized when people begin using silicone in place of o-rings, designers noticed that the lip produces smoother play by prevented the string loop from coming into contact with the response.
In short, removing the lip will increase friction between the string and the yoyo. The effect will become especially noticeable as the string wears in.