A vendor was sent a 1099 for reimbursements, so really he should not have received one. How do we correct when we have already sent the 1096 paperwork in.

The vendor may have paid you under non accountable plan. In that case, you will report 1099-misc income on schedule C (Form 1040) and claim the expenses. The net income (if any) is subject to 15.3% SE tax.