The reaction between tert-butyl methyl ether and HI leads to the cleavage of the ether bond, resulting in the formation of tert-butyl alcohol and methyl iodide:
\[
(\text{CH}_3)_3\text{C} - \text{O} - \text{CH}_3 + \text{HI} \rightarrow (\text{CH}_3)_3\text{COH} + \text{CH}_3\text{I}
\]
The ether bond is broken by the nucleophilic attack of the iodide ion, producing the corresponding alcohol and alkyl iodide.