Tax issues....maybe

If you recover an expense, you can't deduct it. (Unless, as Roadmedic pointed out, you count the recovery as income, which gets you to the exact same place. X + Y - Y will always equal X, no matter what Y is.)

Again, it doesn't matter what it's for, as long as it's a genuine business expense, such as you have described. The issue isn't whether you should be able to deduct such things, or whether or not the company is a bad company for backcharging you for them.

The issue is: was the backcharge already deducted from gross income?

If it was subtracted the top line (gross income), it's already deducted and can't be deducted again. If it was deducted from the net pay but not the gross income, it can be claimed as a deduction.

The whole idea of tax deductions is to reflect actual net income. The company can't deduct expenses it gets reimbursed for. You can't deduct things that were already subtracted from your gross income.