Uber navigation sent me onto the PA Turnpike before pickup—am I stuck paying the toll?

I'm a new Uber driver and had a situation I'm not sure about.

I dropped off a pax in the Harrisburg/MDT area and accepted another ping shortly afterward. Uber's navigation routed me onto the PA Turnpike to get to the pickup. The rider was not in my car yet—I was still en route to the pickup.

I drive my own car and don't have an E-ZPass transponder, so I'll be billed through Toll By Plate.

My questions are:

• Will Uber reimburse or credit that toll since the app routed me onto the Turnpike before the trip started?
• Has anyone successfully gotten reimbursed for a pre-pickup toll?
• If not, do most drivers just avoid toll roads while heading to pickups, even if it increases the ETA?

I'm trying to understand whether this is just a cost of driving for Uber or if there's a way to handle situations where the app's recommended route includes a toll before the trip begins.