  In this article, we investigate the possible torsion subgroups of twists of
abelian varieties with good reduction. As an application, we prove a theorem
concerning ramified primes over any quadratic extension where odd-order torsion
growth is achieved. In particular, we show that for every rational elliptic
curve and every imaginary quadratic field not equal to $\mathbb{Q}(\sqrt{-3})$
satisfying the Heegner hypothesis no odd-order torsion growth can occur.
