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Yes. This result is contained in my PhD thesis, which is available here (see Theorem 1.1.10). We prove that for any finite abelian group $\Gamma$ and fixed $\Gamma$-labeled graph $H$, there is a polynomial time algorithm to determine if an input $\Gamma$-labelled graph $G$ contains an $H$-minor. The case you are interested in is $\Gamma=\mathbb{Z} / 2 \mathbb{Z}$ and $H$ equals odd-$K_5$. For signed graphs, this result was also obtained independently by Kawawarabayashi, Reed, and Wollan.