I agree that they should bring it in, especially if you've asked them to.
Why won't they?
Is it steps, dirty wheels on carpet, too big to fit in doorway easily?
Perhaps if you know why they aren't, then you can take steps to help - if it is steps, is it easier to fold then bring it in, or separate parts (especially nappy bag etc which can weigh a tonne!).
If it's the wheel being dirty, buy a cheap matt, carpet offcut to roll it onto - the carpet/mat can be rolled up when not needed.
If it won't fit through door easily, can it be folded easily?
If it's them not being bothered to do it, ask them to leave their wallet on top with a note to take the wallet, not the buggy thanks! It will be a major pain if it does go missing, and cause strain when you've asked them not to.