My neighbor "blessed" me with some Elk tenderloins. He suggested that I soak them in ice water to remove some of the wild game taste, then pr

Elk is a blessing, and if there is wild game taste it means the elk was not taken care of after the kill. It should be dressed (bled) immediately and butchered for hauling. Elk is also very, very tender if taken care of correctly.

Love Sam's method! I made milanesa last time someone gave me elk - I didn't soak it, but some time in milk or buttermilk will mellow it out if you think it's going to be gamey - mine actually was not. If you think this might be a regular thing you might check out Afield by Jesse Griffiths - game galore!!!

https://food52.com/recipes/2948-elk-milanesa-with-lemon-caper-bechamel

Do the soaking in icewater for a bit. Then dry them and marinade in a basic type marinade. Vinegar/oil/garlic/herbs/mustard powder/onion powder.

Then truss them up with twine if they're rather loose.
Give them a rub of green peppercorns mashed up with mustard and white wine. Rub that on. (don't forget adding salt and pepper before you do the bondage thing with the twine).

Give it a blast of high heat 400-500 to bake it all on..and then reduce to 325 to get internal temp right.

Okay now you should have a 'log' of nicely crusted and well cooked to med-rare Elk part.

Slice it in disks and plate and use a Chimichurri sauce.

Chimichurri Sauce:
Parsley, lemon juice and/or lime juice, garlic, olive oil, Mint (if you have it). and red chili peppers or red pepper flakes to taste.

I'd serve it with a rice..a seasoned squash...and a latin fruit salad of melon cubes, orange slices, red onions, cucumbers, green chili, dressed with lime/oil/cumin/ and cilantro chopped.

Oh...BTW...Up the dosage of the Mint in the Chimichurri for game meat.

I don't soak mine but I don't think soaking it in milk would hurt at all.
Our favorite way to eat it is to rub the meat with a little olive oil, then salt and pepper both sides, spread Dijon mustard on the top followed by a sprig or two of rosemary (or dried rosemary if that is what you have around). Then bake it in the oven on 350 and either use a meat thermometer to make sure you don't overcook it or check on the meat every 5 minutes. Just remember, you want the meat closer to rare than to medium done because if you overcook it, it will be tough. The key to most wild game is to not overcook it, and because they are very lean they overcook very quickly.
Oh, and I almost forgot the best part. Mix together sour cream or plain greek yogurt and horseradish (use whatever ratio tastes best to you, I probably do about 1/4 cup yogurt to a heaping tsp of horseradish) and use this as a dip for the meat.

If you're not a red meat eater. That's going to be pretty challenging.
While it might be sacralige to a game hunter to make a chili out of a tenderloin.
it might be the beast option for one of the item.
I really like game chili...game tenderloins are a bit gamey.
Game sausage is great too if you make sausage.

Now..if you want to go full tenderloin..hang on and I'll make second post.

Never heard about soaking in ice water. However, some soak game meat in milk for a while to remove, or reduce, the game-y taste. Otherwise, I suggest a marinade. Elk can be pretty tough (it's very lean) so for best result you might want to marinate for several days.