  This manuscript derives explicit factors linking mode-mismatch-induced power
losses, in Hermite-Gauss optical modes to the losses of the fundamental spatial
mode. Higher order modes are found to be more sensitive to beam parameter
mismatches. This is particularly relevant for gravitational-wave detectors,
where lasers employing higher-order optical modes have been proposed to
mitigate thermal noise and quantum-enhanced detectors are very susceptible to
losses. This work should inform mode matching and squeezing requirements for
\textit{Advanced+} and \textit{Third Generation} detectors.
