Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Please read Fatwa: 82701.
This Hadith is an evidence for the purity of what remains after the cat if it drinks or eats from something. This is the opinion of Al Shafie, Malik and Abu Hanifa.
But the majority of the scholars are agreed that the cat's urine is impure. Al Nawawi said: "As for the urine of the animals whose meat is unlawful for us it is impure according to the majority of the scholars. The dung of the cat is also impure".
So, we advise you to take care from the urine and the dung of the cat and to clean any place that is touched by them.
Allah knows best.