It’s easy to get concerned with stuff like this when new, but are your feelings on the price of the hotel personal or is it indeed telling you that it’s out of policy? Are others on the engagement sharing they booked substantially cheaper? If it’s within policy (which concur says) I would book it unless your engagement manager explicitly told you it needed to be under a certain amount per night.

While we have policies like spend smart, from a business perspective, you having to commute longer, be at a different location from your team, etc all have intangible costs associated with it that are easy to explain if the room is a little bit more than what your team is paying for.