We prep floors with removing the staples and applying an oil based odor and stain blocker such as Kilz or Zinsser.

Even with cleaning, carpet traps organic matter and odors.

They are not required to clean for your showings.With that many cats and that much noticeable odor there is most likely pet damage in the unit.

That faint odor was probably a little garlic mixed in for good measure. 

Someone told me females can sense odors better than males.  

Examine the septic system for flooding or unusual odor.?

The higher end homes with higher rents are more likely to have inquiries from those who plan farther ahead, some may be looking to move in 60 days or more and you want someone sooner, or they may be downsizing from a 5/4 with kids going to college, and would like to rent but the dates are tied to their present homes' closing dates.I also found out they are more likely to frown upon seeing homes while rented, the current tenant belongings all scattered with packing boxes, dirty clothes piling up in the laundry room - odor...is one thing, the idea of their home being visited frequently by applicants during their last month of stay is the other.It is probably very locale specific thing but some homes I never show while occupied.

Does anyone know how to remove pet odors from carpet?

I just recommended another poster try it to seal in pet odor (before resorting to tearing out ceramic tile) and then felt bad because I had no long term experience....Other than knowing it is a Custom product has been available for decades, but that doesn't always mean much.

If pets or smokers or hoarders are in the unit, be prepared to replace the carpet and carpet pad and odor seal the floor below too when they move out.