Towel hook in bathroom ceramic tile grout
Fixing this could take several directions. 

If you have access to the other side of the wall from where the hook was mounted it may be feasible to open up the drywall from that side and install some wooden backer between the studs that can accept slightly longer screws from the tile side. Fixing up and re-finishing an access hole in drywall would be be far easier that trying to re-work the tile wall. 

The size of the face plate of the hook looks like it would cover up a bit larger hole made between the tiles. Such hole may actually need to chip away at the edges of the tile some too. With a larger hole you can push through a fastener called a toggle bolt which would anchor to the opposite side of the wall material in the mount area. If you choose to use a toggle bolt approach consider applying a ring of silicon sealer between the bracket and the tile on the back side of the bracket. When this sets up it will take up the sheer load on the hook. Toggle bolts work best for pulling the load directly up to the wall and the hook could slide around on the wall due to the larger hole size and force that was parallel to the wall surface. The silicon can help prevent that problem.



Use care in how you go about enlarging the hole as you could end up cracking the tile if you try to force a regular style drill bit into the grout line. A small diameter tile hole drill would be recommended.

For this application I would discourage the use of other types of expanding wall anchors such as the cheap plastic things you press into a hole before applying the screws. They will eventually fail in much the same way as your current fail.