Excel 2013 issue

This is almost certainly a file version control issue, i.e., user error. Excel doesn't retain deleted data; it can't pop back. Double check all your file names. Your description says you saved it for 2016, then saved it again with a new name. You are probably getting the names mixed up somehow.

Go to Windows Explorer to see a list of files. Make a copy of the 2015 file, giving it an appropriate name for 2016. Then double click the 2016 file to edit in Excel, delete the data, then save and close. Now you should be in a clean state. Open the 2016 file again and the deleted data should still be deleted.