The company doesn't appear to have been recording screens, nor intend to in the future.
But Apple expert LucaTodesco is concerned that hackers could use the app's special access to their advantage, telling ZDNet:
It paints a pretty big target on top of the app.
I find this very frightening and dangerous.
This is the latest in a string of Uber-related privacy issues. Earlier this year, The New York Times reported that Apple threatened to kick Uber out of the App Store after it was caught tracking iPhones after the app was deleted.