To try and explain more clearly, maybe a photo or two will help. I'm afraid I don't have a freshly done jar which would illustrate it even better.
The mesh is cut just slightly larger than the mouth so that it will fit into the jar with a slight bit of bending and will sit on top of the vegetable matter just where the neck widens into the body of the jar, at the shoulder, maybe? Because the mesh is a strong plastic and because it is just that little bit bigger than the neck, it stays in place really nicely.
If I was going to cut one out, I'd probably use the canning ring for the jar and cut on the outside edge of that circumference. It's about 9 cm or a scant 4 inches maybe.
I'm not saying this is the only way to do things, I'm just saying it's a method used by a woman here who teaches fermenting and I thought it was fairly elegant. After the mesh is put in place, the MasonTop Picklepipe can be used to release gas.
Edited to add: The cheese mesh is a durable, food-safe plastic that can be re-used. It can be cleaned in a dishwasher or by hand.