  The non-orientable 4-genus of a knot $K$ in $S^{3}$, denoted $\gamma_4(K)$,
measures the minimum genus of a non-orientable surface in $B^{4}$ bounded by
$K$. We compute bounds for the non-orientable 4-genus of knots $T_{5, q}$ and
$T_{6, q}$, extending previous research. Additionally, we provide a
generalized, non-recursive formula for $d(S^{3}_{-1}(T_{p,q}))$, the
$d$-invariant of -1-surgery on torus knots.
