I'd probably accommodate the request on this project and treat it as a process lesson going forward.
From your description, the floor protection isn't really the issue—this customer seems to want a higher level of detail and certainty throughout the project. The fact that they were focused on quote language and niche details early on is usually a sign.
For me, the bigger takeaway would be to document these expectations up front in future contracts so there's less room for interpretation later.
Sometimes the easiest path is to finish the project strong, keep the relationship positive, and use the experience to tighten up your process for the next job.
