Should I reimburse my employees who deny their company-provided health benefits?
Legally, you are not required to do anything. In fact, some companies actually require that employees who have access to coverage through their spouses obtain their medical insurance coverage that way--versus using the insurance offered by their own employer.
Having said that, many employers do offer an offset to employees who either choose to buy their own health insurance coverage or who access health insurance coverage through their spouse's employer's coverage.
You may want to pay people who do what this employee is doing an amount equal to say 50 percent of what you would be paying for her coverage if she were to stay on the insurance that you offer.
But, again, this is just a suggested amount. You can do anything you wish--including doing nothing at all.