  From the link Floer complex of a link $K$, we extract a lower bound $t_q'(K)$
for the rational unknotting number of $K$ (i.e. the minimum number of rational
replacements required to unknot $K$). Moreover, we show that the torsion
obstruction $t_q(K)=\hat{t}(K)$ from an earlier paper of Alishahi and the
author is a lower bound for the proper rational unknotting number. Moreover,
$t_q(K\#K')=\max\{t_q(K),t_q(K')\}$ and $t'_q(K\#K')=\max\{t'_q(K),t'_q(K')\}$.
For the torus knot $K=T_{p,pk+1}$ we compute $t'_q(K)=\lfloor p/2\rfloor$ and
$t_q(K)=p-1$.
