Hi
We stayed in Old Alykanas in Zante 2 years ago and we saw lots of rats! Our villa was next to a field and across from a market garden so they were bound to be there. We saw them running in & out of broken water pipes next to our villa and we also had one on our patio! The village cats didn't really seem to bother with them I think the rats were too big for them!!
We also walked in to Alykanas most evenings and saw lots of squashed rats on the road.
We have been going to Greece for the last 16 years and have only ever seen the odd rat at night when it was dark but the rats in Zante were out in broad daylight!
I would say that we were aware of them but they didn't spoil our holiday in any way, and we didn't see them on our beach so don't worry, forget about them and enjoy your holiday.
Diane
ps the rats didn't put us off Zante but the fact that it's very commercialised did!!