Along with that is the question, can someone purchase (non-travel) on a project if they don't have effort on the project?
I am curious do other teams check the effort before approving each travel reimbursement or do you count on the PI's signature as confirmation or spot check or etc.
In your case, if they were paid one day in July what was that for? Was this all they were paid in July or was it for a specific reason (like travel back then?)
What does this travel relate to? Does it relate to work to be done on that day - like meeting with a subject in a home? If so, what is their employment history - why are they not paid for that travel - or are they paid elsewhere?
If the traveler is not providing effort to that project during that effort period, it is then dependent on the traveler's role on the project and how federal regulations must be applied: