Answer: $8$. Example: We part the table to $T$ tetrominos. After that $3$ of grasshoppers jump to the center, the grasshopper at center jumps anywhere so $2$ of $4$ squares can remain empty. Assume that $9$ or more squares can remain empty. Then $7.2<16$ so there exist a square which has $3$ grasshoppers after jumpings. Also $3.1+2.6<16$ so there exist atleast $2$ squares which has $3$ grasshoppers. If a square has $3$, then it should be in center $2x2$. Also its all neighbours should jump to that square. But if there exist $2$ squares which has $3$ grasshoppers, then $2$ grasshoppers should jump to $2$ squares which is impossible (they have $2$ same neighbours). So $ \leq 8$ squares can remain empty.