I worked for a place that did this, i.e. added a delivery surcharge which the house kept. I discovered that this is, in fact, illegal in my state unless it is disclosed in writing. Which it wasn’t.

When we had a new point of sale system installed, as our restaurant’s resident tech person I naturally adjusted the such that were were in compliance with the law and delivery surcharges were pooled with the employees’ tips.

The owner never noticed.