Cores are no different than deposits on cans or bottles. The parts have residual value and that’s reflected in a core charge. If the exchange to the end user takes place in a single transaction, then the core charge exchange should also be transparent to them. That being said…
The trend in all businesses seems to be full disclosure and itemizing every last thing. So a core fee for a part might be listed but then subtracted back off if the old parts are not taken by the car owner. What might appear instead is a handling fee. Someone has to take that old core back to the merchant that charged the core fee in the first place and the back office work to resolve the billing. In the old days, all that may have been bundled into the hourly rate or parts pricing. But with competitive pricing comes itemization. Otherwise, your prices may APPEAR higher than the competition and end up losing business to price shoppers…