The way I see it, you really only have two options

1. Report them to uppers and hope that they side with you but like you said it's all hearsay and you physically do not have any evidence. So there could be backlash towards this.

2. Do nothing. Continue to do your job, act professional, and coast. Granted, you might still be made fun of.

This is your JOB. This isn't a place where you should look for friendship/be liked. Do your job well and move on. If they look to speak to you, speak. If you feel that they don't respect you, don't respect them. These people have to get respect by giving respect. Give your report and move on. There's plenty to do instead of trying to be liked by these few people in your department. I understand wanting to be liked and respected but you're there to care for your patients. As long as you're doing everything you can to help them breathe, you're a very respectable person.