Popping in the dash

I apologize if this is elsewhere, but I cannot find the search function. I have a 2011 Prius with a popping noise in the dash when I move the air from the vents to the defrost or vice versa. I researched this online and found the gear in the photo is loose on its shaft. I pushed it back on and the popping went away. I fear, however, that this is going to ultimately break. I cannot access it to see what is wrong as the structure that houses the blower fan and cabin air filter blocks it from being removed. I cannot see how to get to it or what the root cause of the problem is. Has anyone dealt with this issue before and have any knowledge of how to access it or what is the issue(s) causing this? I thank you in advance for your assistance.