Per the
HGP terms and conditions, your benefit includes free breakfast, tax, and tip at full-service Hyatt properties:
5. In Hyatt hotels that do not have a Regency Club or Grand Club lounge, daily complimentary full breakfast (tax and gratuity included) will be provided to the member and each guest registered in the room, maximum four (4) people. For stays at Hyatt Regency Bethesda, daily continental breakfast (tax and gratuity included) will be provided to the member and each guest registered in the room, maximum four (4) people.
That means when you dine, all charges are taken care of. When the check arrives and there is a space for gratuity, that is there for you to specify any amount
over and above the normal gratuity that HGP is paying, which will be added to your folio.
In most cases, I simply write "included" on the tip line and sign my name. For cases where I do tip (on breakfast-included rates like AAA), the tip amount shows up on my folio as a separate line item.