Oh! That makes sense, the two roses I found these on are grafted on fortuniana. Thank you!

Tear them out of the socket rather than cutting them, or they will come right back.

Suckers give trouble and take over the plant if not removed.

Thank you for the advice! I'll have to check my other plants to see if they have any suckers, this is the first time I've noticed them. I'll be sure to tear them out instead of cutting them this time too!

Definitely, without a doubt, that's a fortuniana sucker. Just break them off at the base. They should snap right off easily. They are easy to identify luckily with their signature pointy leaves.

May I ask where you purchased this rose?

I purchased this rose (Melody Parfumée) from a local nursery called Plant Ranch Nursery. I don't think they grow their own roses though. Most of the Fortuniana roses I get from local nurseries or hardware stores seem to come from Nelson's I think, since there's usually some sort of Nelson's sticker on the pot.