Eater of Days, Hushwing Gryff, and the stack
The opponent can use either spell to target Hushwing Gryff while Eater of Days is on the stack.  In this case,


The spell resolves first, removing Hushwing Gryff from the battlefield.
Eater of Days resolves, and as there is no Hushwing Gryff on the battlefield the caster of Eater of Days loses two turns.