The ornamental design for a grillbrush handle, as shown and described.
FIG. 1 is a top perspective view of a grill brush handle showing our new design;
FIG. 2 is a front elevation view thereof;
FIG. 3 is a left side elevation view thereof, the right side being a mirror image; and,
FIG. 4 is a top plan view thereof.
The broken lines in FIGS. 3 and 4 represent the bounds of the claimed design while all other broken lines are directed to environment and are for illustrative purposes only; the broken lines form no part of the claimed design.