Workbook password protected in Excel 2013, re saved in earlier version protection removed

I have created a workbook in Excel 2013 that is used by my clients to calculate their payroll for them. I hide certain tabs that contain the bulk of the formulas used to create the calculations, and lock most cells in the worksheets that are to be used by my clients, allowing them to only edit portions that they need to in order to adjust their payroll (change hours, rates, etc). The workbook itself is then password protected to prevent them from interfering with the formula's on the hidden tabs. I save it as a 2013 file, then email it out to my clients, some of whom have earlier versions of excel (one had Excel 97, as an example, others have 2003). Once they have opened, and then edited the fields they need to, they re save the file, this time as an earlier version, and send it back to me, and when I open it up and go to unlock the workbook and sheets, Excel does not ask for me to enter the password, it just unlocks it with a click on "Unprotect." I am worried that this means my workbook is really not that protected, if it means all someone has to do is open it using an earlier version of Excel to wipeout the protection. I've also noticed this happening to greater effect when I share my workbook with Mac users, only on those occasions, the entire workbook comes back with all tabs unhidden and unlocked, with all password protection removed. Can you please tell me if there is a way I can prevent this from happening? Thank you.