Reptoids thermal isn't that good, so more smoke works. In fact this was a trivial-ish mission when they were still armed with gauss.
This now - with at least personal/cyber armor isn't too bad, but losing a few guys is likely, so I'd bring expendable guys or pass until better tech - the loot isn't worth it, most UFOs are easier and grant better rewards. Reptoid assassination /w dogs / rookies is probably easier, too.
Going at night can work in your favor for initial smoke setup, but makes it harder to spot straggler aliens, for which you'll probably need to lit entire map in flares, or have veteran critter with 20+ night vision to sweep the map.
The easiest (but boring) way to beat it (and almost any other mission, really) is to use smoke & grenade cheese tactics: hide in smoke, spot with bats (100% thermal, making everything a cakewalk) / rats (70% thermal, 1 psi) / scout bots (50-65% thermal, all much better than reptoids) and chuck grenades. Grenades don't trigger spotter and mean you can remain in smoke safely, unless directly seen.
If using guns, the only 100% safe tactic is hit & run from transport, being unseen via night or smoke, as not to trigger reactions. Shooting and running back the Kitsune ramp needs high TUs, thus most likely synthsuit or advanced soldier transformation.
Skymarshall has doors in the back, but they're small and IMO even more awkward to use.
Lacking that, can set up ambushes from smoke, trying to kill as much aliens as you can in a turn, then going silent for a turn and trying to survive the pushback.
And lastly, can just shoot from smoke, triggering spotter and praying to RNG to not get hit back. Chances to be hit through smoke are decent, but not that high.
Reptoid pistol shots will deal ~23 damage on average to personal / cyber armor, cooking your guy in 2-3 shots. Fairly decent survival rate if you only allow rare hits.
Tanks will get ~15 front damage on average, cooked in ~6 shots.
Juggernaut suit will bounce off pistol shots on average. Can get it early from underwater.
Rifles and Heavy breaths are more dangerous, but also rare'r, so those are priority targets.
Mind control trivializes most missions - this one too, granted you're nearing 90PST/60PSK hybrid to be able to MC reptoids.
There's also way to end mission early by shooting rocket into "controlling" altar in the tower - but I only managed to do it once and wasn't able to reproduce again.