Answered by Ustadha Shazia Ahmad
If one enters a bathroom and uses the toilet paper that is available to clean oneself (before washing with water), and learns that the toilet paper, after having used it, contains some sort of moisturizing cream – is there any reason for one to be concerned that one has not made a proper istinja? Or is it that even if the paper does not somehow meet the requirements of istinja – the water in itself suffices?
In the name of Allah, the most Merciful, the most Compassionate
If one used water after using this toilet paper, then one’s istinja (washing after using the lavatory) is valid. Toilet paper in itself does meet the proper requirements for istinja as long as the conditions are fulfilled. Otherwise, water is necessary. Those conditions are as mentioned in the Reliance where it says (e9.5):
But it is obligatory to wash oneself with water if [s.and not just toilet paper]:
1) one has washed away the filth with liquid other than water, or with something impure;
2) one has become soiled with filth from a separate source;
3) one’s waste has moved from its place [of settling after exiting] or has dried;
4) or if feces spread beyond the inner buttocks (N: meaning that which is enfolded when standing) or urine moved beyond the head of the penis, though if they do not pass beyond them, stones suffice [s. or toilet paper suffices].
Another condition that is not explicitly mentioned above is that the toilet paper that one wipes with must be dry if one wants to confine oneself to wiping. If the toilet paper mentioned in the question was actually moist, then one’s wiping would not be valid if one confined oneself to the toilet paper and did not use water. If it was not actually moist, but merely contained some moisturizer that had dried (this is probably the more likely case), then this would not affect the validity of the wiping.
 This translation has been modified slightly from the original wording in Reliance for clarity.