In the holomorphic strip case, assume $v_{1},\ldots v_{n}$ are in the kernel of the linearized Cauchy-Riemann operator on $W^{1,2;\mu=\pi}$, such that $\Omega(v_{1},\ldots v_{n})$ does not vanish identically. Then $\deg q-\deg p\geq 1$. When the equality is achieved, the holomorphic strip is an immersion up to the boundary with minimal vanishing at the corner, and the zero dimensional moduli space is regular.