An $\mathrm{S}_{\mathrm{N}} 1$ reaction involves two steps; formation of carbocation (which is the slow and thus, the rate-determining) and attack of the nucleophile on the $\alpha$ - carbon.
Among the given options, the $\mathrm{C}-\mathrm{X}$ bond is weakest for $\mathrm{C}-\mathrm{I}$ in $\left(\mathrm{CH}_3\right)_3 \mathrm{C}-\mathrm{I}$.
Thus, it will be most reactive towards $\mathrm{S}_{\mathrm{N}} 1$ reaction.