Placing a long pass filter (e.g. cut-off 500 nm) before the emission monochromator should help.

I think you want to put a cutoff filter between the excitation monochromator and the sample. That way, the 620 nm 2nd harmonic light from the excitation monochromator set at 310 nm will be absorbed, but the 310 nm light will still strike the sample and the 610-640 nm emission will not be contaminated by the 2nd harmonic light.

I was able to do that in my setup with an orange filter. It cuts everything bellow 600nm and passes everything above. My excitation is with 395nm LED, and with filter, the 790nm peak is gone.