What do the Teeth on the SpaceX Falcon Mod4 do?

Question

Can someone explain the purpose of the 'teeth' seen in the last picture of this answer?

Do they have a specific name? They look too far up to be used to grab anything since the rockets land vertically on their base.

Answer 1

tl;dr - Better aerodynamics at high speeds.

There is a paper that compares the plain grid fins with locally swept "toothed" grid fins:
Novel High-Performance Grid Fins for Missile Control at High Speeds (PDF).

To quote a part of its conclusion (emphasis mine):

The results show an essential reduction of the drag for the locally swept configurations. The most important results can be summarized as follows:

• The gained profit for the investigated realistic locally swept lattice wing configurations in comparison to the conventional ones in the zero-lift total drag amounts up to 38% and in the lift-to-drag ratio up to over 20%.
• The lowest zero-lift wave drag is shown by the lattice wing construction with the peak-type of locally swept lattice wings (LSLWp and LSLWp2). On the contrary, better lift-to-drag performance at wing incidence is shown by the valley-type of LSLW (LSLWv and LSLWv2).
• The effect of the LSE increases above all with the free stream Mach number, the local sweep angle, and the relative thickness of the members and the bluntness of their leading edges. It decreases with the incidence angle and for bigger relative tooth-sizes.

Or, in non-scientific-paper-speak: The toothed grid fins are better than the flat grid fins as they have better zero-lift drag and a better lift-to-drag ratio.

Essentially it's for the same reason fighter jets have a swept delta wing design.