Differential systolic inequality for embedded one-holed tori

Let $K\subset {\mathbb{R}}^N$ be an embedded torus with one boundary component, and suppose that $\partial K$ is a unit circle. A closed curve in $K$ is non-null-homotopic if it is not null-homotopic in $K$. Differential systolic inequality. There is a non-null-homotopic closed curve in $K$ of length $\ell$ satisfying

$$\ell^2\lesssim \operatorname{area} K-\pi.$$

This inequality is proposed in response to a possible counterexample to the quadratic pants decomposition conjecture obtained by iteratively adding scaled copies of a one-holed torus to a cube. The implicit constant is not stated to depend on the genus and the conjecture is presented as an open potential remedy for that construction.