As a contractor/sub-contractor you are a 1099-MISC worker. I would categorize the expenses as meal & entertainment as you have already stated and any reimbursements for the meals & entertainment would be considered income for the job. There is no pass through account to categorize the income. The transaction becomes a wash. A break even for the meals & entertainment.
If you would like to take it even a step further you can allocate the reimbursement for meals & entertainment directly to the meals & entertainment account. This will decrease the meals & entertainment expense.
Not to derail this important conversation, but is "pass-through expense" a common industry term? I hear it often but we had another discussion in the community some months ago about its usage.