  To elucidate the mechanisms behind the enhanced $T_c$ in monolayer (1ML) FeSe
on SrTiO$_3$ (STO), we grew highly strained 1ML FeSe on the rectangular (100)
face of rutile TiO$_2$, and observed the coexistence of replica bands and
superconductivity with a $T_c$ of 63 K. From the similar $T_c$ between this
system and 1ML FeSe on STO (001), we conclude that strain and dielectric
constant are likely unimportant to the enhanced $T_c$ in these systems. A
systematic comparison of 1ML FeSe on TiO$_2$ with other systems in the FeSe
family shows that while charge transfer alone can enhance $T_c$, it is only
with the addition of interfacial electron-phonon coupling that $T_c$ can be
increased to the level seen in 1ML FeSe on STO.
