We report on a novel two-photon excitation stimulated emission depletion (2PE-STED) microscope based on time-gated detection. The time-gated detection allows for the effective silencing of the fluorophores using moderate stimulated emission beam intensity. This opens the possibility of implementing an efficient 2PE-STED microscope with a stimulated emission beam running in a continuous-wave. The continuous-wave stimulated emission beam tempers the laser architecture's complexity and cost, but the time-gated detection degrades the signal-to-noise ratio (SNR) and signal-to-background ratio (SBR) of the image. We recover the SNR and the SBR through a multi-image deconvolution algorithm. Indeed, the algorithm simultaneously reassigns early-photons (normally discarded by the time-gated detection) to their original positions and removes the background induced by the stimulated emission beam. We exemplify the benefits of this implementation by imaging sub-cellular structures. Finally, we discuss of the extension of this algorithm to future all-pulsed 2PE-STED implementationd based on time-gated detection and a nanosecond laser source.