Transmission fluid leaking into radiator?

This is definitely oil but I would not suspect transmission fluid on this vehicle. The transmission oil cooler is part of the radiator so unless this has failed, I doubt it is transmission fluid. Is there a reason they are saying it is transmission fluid?

If it is engine oil this guide will help. However, have you checked the transmission for coolant as well?

https://www.2carpros.com/articles/coolantantifreeze-in-the-engine-oil

Usually it's due to a leak inside the radiator that lets transmission fluid mix with the coolant, but in less common cases it can be due to a leaking head gasket that lets engine oil mix with the coolant. If that happens you will usually see signs of coolant in the oil too. Water dripping from the oil cap is a sign of condensation from a lot of short trips when the engine doesn't have time to warm up. A whitish or chocolate brown color to the oil indicates coolant is in it.

If it's transmission fluid that's mixing, that is not harmful to the cooling system as long as it is corrected soon. The system should be flushed and refilled with clean coolant. Petroleum products in the coolant will rot rubber hoses over time leading to leaks. The problem is at some point, for sure when the hot engine is turned off, there will be higher pressure in the cooling system than in the transmission cooler part of the radiator so coolant will go into the transmission. That will deteriorate the seals and clutch plates. This is one time a transmission flush is a better choice than a simple filter change and refill.