Lens Cleaning help needed

I’m still learning

I am delving into servicing my own 35mm equipment and recently took apart a rokkor 50mm 1.7 MC lens to clean. Easy enough but on one element I foolishly used lens cleaner and it left “cleaning marks”. I tried polishing it with a dry micro fiber cloth to little effect. Am I correct to assume that I have encroached upon a lens coating that was supposed to have been left alone?
A couple additional questions: when and how can a lens cleaner solvent ( like Zeiss) be safely used and how to know? Is there anything to be done to that troubled element now?

I doubt that you've hurt the lens coating. You probably just put too much lens cleaner on it. Let it dry and try using your breathe and wipe quickly. It will probably take several tries. Micro fiber clothes are useful for some things but they are not absorbent. Use lens tissue, which is.

I'll recommend this YouTube channel, https://youtube.com/@mikeno62?si=Vl7eACnO7UL2TiT_

as this guy has, IMO, the best information of practical camera lens cleaning.

I think it was from one of his videos that I started using Eclipse lens cleaning solution, which is fantastic as part of his rehabilitation of optical glass.