Popping these tiny blisters release some nasty oily liquid.
That sentence is going to give me nightmares.
My wife's cat escaped from the dungeon and peed on a guitar tuner pedal of mine. Stripped the powder coated finish right off of the aluminum. Nasty stuff, cat urine is.
You might try moving up the scale of eco-unfriendlyness until you find something that works better. Some things I can think of to try (test in a small area first, duh):
Not-so-bad ideas:
You might experiment with dilute acid (distilled vinegar) and base (lye), separately, of course, to see if either has an effect. Always add acids (and strong bases) to water, not the other way 'round.
Pet-stain-remover
Oxidizing cleaner (Oxyclean is a popular brand in the USA market for these types of cleaners)
Isopropyl alcohol
Electrical contact cleaner (this is generally good for getting stains off of plastics without melting them - CRC makes a good one in the USA)
Less-bad bad ideas:
NON-CHLORINATED brake cleaner
MEK (this
shouldn't melt the carpet)
Bad ideas:
Carbon Tetrachloride (carcinogenic, but it will fully evaporate - wear a respirator and open the windows)
My money is on Oxyclean.