The pet parent can request a contribution to utility bills from the sitter during the sit.
Although rare, this usually only happens on longer sits, but the pet parents can request it for any length or sit, as long as they are upfront and transparent about it on the listing and in their first contact messages with the sitters.
They should clearly agree which utility bills the sitter will be paying, how they will be paying the bills and by which date/s before the sit is confirmed.
The sitters and/or pet parents can take the relevant meter readings on arrival at the sit and at the end of the sit to accurately record what they have used. A recommendation is to take photos of the meter readings with a time and date stamp on them.
TrustedHousesitters are not involved in any of the above, this is a private arrangement and all agreements are directly between the sitters and the pet parents.