A couple things…
One, I’m a pizza cook, in my 30’s, and pay almost half of my check in child support. I’m also honest, hard working, and would sure hate to lose my job, not to mention my child’s support, for no reason. Jobs are tough to find these days. If you really don’t trust someone on your staff then that’s another story, and no one can make that call but you. I appreciate that your in a tough spot, but you also owe that staffer a fair shake.
Two, before finding the opportunity to start over in a bigger, better pond (with a much higher ceiling) I managed a small but very popular and successful pizza pub. Here’s the deal; anytime management, in any form, takes possession of the staff’s tips, management needs to be responsible for them. They need that money. That’s what gets them to work and hopefully keeps a smile on their face when their dealing with your customers. If for whatever reason they are not in the jar (where you can bet the staff would keep an eye on them) then they need to be locked up in the safe. You need to correct this and I would strongly suggest offering some type of a comp to your staff.
This is a managerial short-sight, easily correctable, and no grounds to terminate an employees meager income.
You know that.