  It was proved by Mineyev and Yaman that, if $(\Gamma, \Gamma')$ is a
relatively hyperbolic pair, the comparison map $$ H_b^k(\Gamma, \Gamma'; V) \to
H^k(\Gamma, \Gamma'; V) $$ is surjective for every $k \ge 2$, and any bounded
$\Gamma$--module $V$. By exploiting results of Groves and Manning, we give
another proof of this result. Moreover, we prove the opposite implication under
weaker hypotheses than the ones required by Mineyev and Yaman.
