Chewbacca
I have my GC here in my home a lot and I have very similar house rules as MissAdventure. I don't expect anyone to wander around my house with food, jump up and down on my furniture, damage my flooring or cause any damage. Having toys strewn all over the floor doesn't bother me at all, so long as there's no trip hazard to anyone. The odd bit ofwailing or crying is to be expected occasionally with small children but I don't expect, or want, full on screaming melt down for days on end; that's horrendous for everyone concerned and I'd expect the parents to deal with that promptly (I'm fortunate that it's never occurred). On reading through some of the posts on this thread, it looks as though I'm a strict granny in comparison to some; possibly so but children, just like adults, are never too young to learn about respect for others and themselves.
I also, until they moved a year ago, had my grandchildren at my house frequently and from a young age. They learnt and understood very quickly what was and was not allowed in our house and they stuck to that whether with their parents or not. When looking after them at their house we stuck to the norm for them there apart from a couple of things I found dangerous so I just said "that's OK if Daddy and Mummy are here, but Nanny doesn't like it, so not whilst I am looking after you!" Again very quickly accepted!
I think having them from a young age and regularly, helped them to understand different behaviours in different places or with different people which I think was a good lesson. I rarely see them now but notice that when they do on rare occasions come to our house they slip in to Nanny's house expectations without even needing a reminder. Yes like you Chewbacca I might come over as strict but in fact I think the kids felt/feel secure because expectations are clear. And the "rules" were reasonable and the reasons for them (safety, not ruining things etc) were all clearly explained.
I think for the OP it's a bit harder as they have not been regular visitors from a young age. I wouldn't send an email though, I would talk about expectations in a chat!