Neither a block nor a grapple can ever reduce the targets capacity to dodge. So in your case, they would have to dodge with their full capability against the 4 shift attack.
If your opponent wants to attack you, while under the influence of the block to movement, they can a lot of times do so without being hindered. If they have a gun, they can shoot at you without having to overcome the block. If you are in the same zone, they can hit you without having to overcome the block.
The block only comes into play, when they are trying to move. If you are in a different zone and they want to get to you, they'd have to do an athletics roll against 1 (to move a zone) + the block against movement or be stuck otherwise.