Would you explain the parts I underlined in the sentence below?

I (a desk clerk) pick up the phone and ask the guest if he has another way to pay for the incidentals or the room for that matter, because his 3rd party billing is up and we've got to move on here.

Contributing Member1,410
Incidentals = other charges (phone, snacks from the room refrigerator, hotel restaurant charges, etc.)

3rd party billing = his bill is being paid by someone else (probably his company).
Veteran Member114,974
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great! thank you, always,