Perhaps you could try spraying the cat tree with this solution (of course when the cats are not around):
Lightly Lavender Antibacterial Spray
* 1 cup water
* 20 drops pure essential oil of lavender
Pour the water into a spray bottle. Add the lavender essential oil and shake to blend. Spray on the surface and let set for at least 15 minutes, or don’t rinse at all.
Makes: 1 cup spray
Shelf Life: Indefinite
VERY IMPORTANT: Make sure the cats do NOT come in contact with the undiluted essential oil.
It's a natural remedy I often spray the kitchen counters with, because they babies always jump up there. I have never had any negative reaction (as in allergies or such) from the cats while using it.
From www.care2.comQuote:
New research is proving that the old folk recipes using herbs and essential oils to kill germs, such as those used by 14th century doctors during the Black Plague, were based on good science. Many essential oils, such as the oils of lavender and thyme, are more antiseptic than phenol, the industry standard. Research is also showing that antibacterial plant oils may not cause drug resistance as could be the case with common chemical disinfectants.