Can a company withhold pay to reclaim monies that were labeled as “reimbursements”?

Typically, a reimbursement cannot be reclaimed, either--a reimbursement is usually the company reimbursing the employee for a work-related expense which the employee had to bear (e.g. put on his/her charge card). Usually, the only monies which I company may recoup are "advances" which are not in some paid off by the employee's work (e.g. an advance against sales for a sales rep, if the rep then doesn't sell enough to cover it). Or a loan--sometimes a company will loan an employee money, to be repaid like any loan.

Regardless of the name used, monies may only be recovered if there was a mutual understanding between employer and employee at the time the money was issued that it was to be repaid. Furthermore, the employer may not simply debit money from a paycheck without the employee's consent. Based on what you write--money taken out of pay; the fact that you did not understand that the money was to be repaid--you may have a legal claim against your employer to recover any money taken to date and to stop them from doing this. But to enforce any claim, if you can't work it out voluntarily, you'd have to sue them; and obviously, suing your employer can have negative effects on your career, in many cases up and including termination of employment. Before acting, think carefully what you are willing to risk for the amount of money involved.