The ornamental design for a basketstrainerholder, as shown.
FIG. 1 is a front right isometric view of a basket strainer holder showing my new design;
FIG. 2 is a front plan view thereof;
FIG. 3 is a bottom plan view thereof;
FIG. 4 is a top plan view thereof;
FIG. 5 is a right side plan view thereof;
FIG. 6 is a left side plan view thereof; and,
FIG. 7 is a back plan view.
The broken line showing of the bottom portion of the basket strainer holder is included for the purpose of illustrating environment and forms no part of the claimed design.