= Solution
View each of the three level-one triangles in $G_2$ as a copy of $G_1$. Observe the walk only when it moves from one corner of such a copy to a different corner. By symmetry, the next of the two other corners is equally likely, so this embedded chain is the simple random walk on the coarse graph $G_1$. Part (a) says it makes an expected five coarse transitions before reaching $B$ or $C$.
Within each level-one copy, the mean time for one coarse transition is again five by part (a). The <Strong Markov property> at successive coarse-corner hitting times therefore gives
$$
\boxed{\mathbb E_A T_{BC}=5\cdot5=5^2=25}.
$$
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