SQL Server: can dynamic data masking be safe when providing a database backup?
No, I'm sorry. Your partner has a sysadmin login for their SQL Server, and a sysadmin can do everything with everything inside a SQL Server instance - including the databases.

I suggest that you develop a routine to clear out the sensitive data. I.e., perform the backup. Restore it to a different database name, clean it. And now produce a new backup.