Thanks for reaching out to me in the Community, @pamlaplant.

No, this won't interfere with your employee's payroll totals and taxes. The purpose of performing this process is only to remove the paychecks you've already printed but still showing from the print queue. Please refer to the screenshot I've attached above.

Your employee's payroll totals and taxes will only be impacted once you delete some cashed out paychecks that shouldn't be deleted.

Feel free to leave a comment below if you have additional questions. I'll be glad to answer them.