Mechanism of SN1 reaction
Surely there are both $\ce{H2O}$ and $\ce{OH-}$ which attacks the carbocation, as well as, heaven forbid, $\ce{H3O+}$ (and countless other species formed by the auto-ioniziation of water).

Usually textbooks record $\ce{H2O}$ as the attacker because it is much more abundant in the mixture.

After that, usually another $\ce{H2O}$ comes and take away the extra $\ce{H}$ with itself converting to $\ce{H3O+}$, but as I mentioned above, this step could also be done by $\ce{OH-}$ among many more species, but the concentration of those other species are too small that they are not worth mentioning.

PS: the last step can also be done by the product, i.e. t-butyl alcohol.