ia the damage at the bottom of the stem, could you use rabbit guards to protect it( or split lemonade bottles) under the bark are the channels that take water and nutrients up and down the plant if badly damaged--especially all round --- if not killing it( it may do eventually) it would weaken it if ithe marks go deep enough if its just light surface stuff and the vine does not look affected then just keep an eye on it but some protection could help

Or wrap a small piece of wire mesh over the section that tey scratch.

good thinking bulbaholic-- i'm more troubled withrabbits who still manage to nibble through the holes!

It would be best to protect if you can - strimmer damage round the base of trees has been known to kill very mature trees because, as Pamg says, the nutrient flow of the plant is in the area immediately underneath the bark - too much damage, particularly if it makes a full circle round the plant, can kill it.