  We use the $O(d,d)$-covariant formulation of supergravity familiar from
Double Field Theory to find the first $\alpha'$-correction to (unimodular)
homogeneous Yang-Baxter (YB) deformations of the bosonic string. A special case
of this result gives the $\alpha'$-correction to TsT transformations. In a
suitable scheme the correction comes entirely from an induced anomalous double
Lorentz transformation, which is needed to make the two vielbeins obtained upon
the YB deformation equal. This should hold more generally, in particular for
abelian and non-abelian T-duality, as we discuss.
