The white shape on the stem end looks like a callus. I have seen this occasionally on the top of cuttings. It will not produce roots or stem, but it won't hurt anything either. I wouldn't cut it off.

That is a relief, thank you! this rose stem means a lot to me. Also you said that you occasionally see them on cuttings. I am curious, how did those cuttings fare-did they successfully mature? and did the callus disappear?

They didn't seem to fare any differently than the other cuttings. As what happened to the callus, I lost track of it when the plant matured. I do a lot of cuttings at a time.

Ah wow I see, thank you!