Please explain a bit more. Where do you live? Why do you travel "to" your tax home (and not away from your tax home.). Where do you actually work for this client?
Note, that in general, all monies paid by your client or customer must be included in your schedule C gross income, even if not reported on a 1099-NEC. Then, you either can deduct expenses or not, depending on the rules. The client should probably not be reimbursing you tax-free (omitting the payment from your 1099) because the client can't take responsibility for how you file your tax returns or what deductions you qualify for.
