  We compute the wonderful compactification of symmetric varieties of
$SL(2,F)$, where $F$ is a finite field-extension of $Q_p$ with $p\neq 2$, that
comes from either an abstract or $F$-involutions of $SL(2,F)$. For each of
those wonderful compactifications we find the $SL(2,F)$-stabilizers of the
accumulation points of the corresponding symmetric varieties and compare them
to the Chabauty limits found in Ciobotaru--Leitner 2022.
