You can't get a refund.
If the employer reimburses your expenses under an accountable plan, then the reimbursement is not included in your gross wages for income or employment tax purposes. However, your employer did not use an accountable plan.
With an accountable expense plan, the employer only reimburses you for expenses that you prove to the employer with receipts. The burden is on the employer to maintain the paper trail and prove, if audited, that only allowable expenses were reimbursed tax-free.
Your employer simply grossed up your wages to cover the expenses. This places the burden on you to claim any deduction, and to maintain the paper trail to prove, if audited, that the expenses were allowable deductions. It also limits your deduction by the 2% rule, and it means that you still pay employment tax on the gross wages.
