
for the first time ever we had this issue with our Inka getting excited at the next doors Russells barking and running their side. She put her head through the panel which had rotted being directly on eh ground, we replaced it as ours had damaged it.
If their dogs get into yours then they should make their end secure.
If your own dog is jumping at the fence ti is likely 6 of one and half dozen of the other.
it might be worth getting some posts and a roll of 2 inch weldmesh or sheep fencing wire and make a fence on the inside of yours about 6 inches in. it need only be about 3 - 4 foot high.
This will avoid your dog being able to get to the fence,a nd if it is damaged it will be obvious it is their doing, but the wire will hopefully keep them out, and also stop the vicious cycle of them egging each other on.
In this way the novelty for both sets of dogs will wear off and any major neighbour issues hopefully avoided for the future.