How can I retouch photos on iPhone or iPad?

Photos iOS on the iPhone has currently no retouch brushes, only enhancements that apply to the complete photo (https://help.apple.com/iphone/11/#/iph96b1e322). The predecessor iPhoto iOS allowed us to retouch small blemishes by brushing across blemishes with our finger tips, but Photos does not yet offer this.

You will need to find a third-party app that offers retouch brushes. Pixelmator, for example, offers some brushes.

I am doing all necessary retouching on my Mac and sync the result back to the iPhone with iCloud Photos.

I forgot the link for the available adjustments on an iPad: Edit photos and videos on iPad - Apple Support. It is basically the same as on the iPhone - you need third-party apps for brushing in adjustments locally (How to edit with third-party apps and extensions in Photos).

Both the iPhone and iPad allow to use the Mark-Up extension to draw or scribble on a photo, but that is not suitable for retouching.

You would either have to suffer with the edit option built in or download a third party photo editing app (ex. FaceTime)