I think this isn't as well known, but using the Frost Bomb (note to others, this comes with the Alien Hunters DLC) on the Warlock will remove mind control on your soldier.
Vigaroe reports this in his well-researched blog on XCOM. I can further attest that I have done this. Vigaroe says that the Frost Bomb will not remove any action points from the Warlock or other Chosen, however.
This option is available very early in the game. The OP reported that Elena was at Colonel, which implies late or possibly mid game. In the mid to late game, you should be able to alpha strike the Chosen within 1-2 turns. That is, every single person focuses fire. If someone is mind controlled and no other enemies are on the map, then strongly consider running to a flank shot or even to point-blank range, abandoning cover if necessary. Obviously you will need to exploit the Chosen's weaknesses. Using the psi operative ability Stasis will shield the soldier for one turn. On other enemies, it should break mind control, but the Warlock's mind control is not affected, per Vigaroe.
If you are at the very beginning of the game and the Warlock is your initial Chosen, the best move is likely to be just avoiding the mind controlled soldier. In Retaliation missions with resistance soldiers active, this could get your soldier shot at.
On Legendary difficulty, where supplies are not a critical shortage and alien corpses are very abundant, I tend to build mind shields for everyone. Building them for just your close combat soldiers, i.e. Templars and Rangers, is probably sufficient. If your Reaper got mind controlled, then, without intending to pile on and blame the victim, consider reviewing your tactics to see if you could have avoided that event. Reapers should be in stealth almost all the time. The skill Silent Killer isn't adequately described in game - if they land only kill shots, they are guaranteed to stay in stealth. I argue this skill is mandatory. If the Warlock was weak to Reapers, then you would contribute by using the Claymore and perhaps Sting (that skill allows one shot which is guaranteed not to break concealment). At lower levels, I do tend to have my Reapers abandon stealth at the end of the engagement, treating them like a sniper with a weaker gun.
The accepted answer mentions that captured soldiers can be rescued. This is not guaranteed to be true in the base game. The game may or may not offer you the rescue mission. If you play the Lost and Abandoned tutorial, you are guaranteed a mission to rescue Mox. This is the only exception. Or you can install the mod Always Recruit and Rescue. Many people play with mods. Anyway, in the base game, if you lost your Reaper, you should shortly get the option to recruit a new one from the Reapers.
A mod that indirectly helps is A Better Militia. This reworks the militia. It nerfs their gun damage and I think it lowers their aim stat. However, it also gives them the ability to use flashbangs, suppression, and overwatch. In fact, militia soldiers tend to prefer these abilities to shooting. They will soften the enemy up. But you will have to finish the enemy off - the author reports that this was their intent. In this case, your mind controlled soldier would be less likely to be shot at, and would take less damage per hit. I haven't been in the author's situation, but it's likely that she would maybe draw one actual shot per turn, with low probability to hit. She might also draw overwatch fire, which comes with a hit penalty.