I was told this necklace was gotten at the Santa Domingo pueblo many years ago

My friends recalled, but weren’t sure, that they got it from a larger man who tended to make larger pieces. It has 18 strings of red coral, and sterling (which is tarnished now because they got it many years ago.)
I do not recognize the hallmark, which is incorporated with the design. See photos. Thank you!

It’s a nice old authentic piece, but I think that what you describe as a Hallmark is just part of the decoration on the sterling collar. Impossible to tell who the artist is or was.
Unfortunately, because of cheap imitations and unrealistic expectancies of modern buyers these older pieces are not sought after as much as they should be. All the findings on this piece are correct for the time and location. I can’t see what it is strung on (should be a linen thread and not wire). Wear with care, or mount it in a Ryker frame for protection and display.
People should also consider making sure they are properly insured for pieces like this.

What do you think it is worth? I would have no idea what to insure it for. Thank you for your help!

Also, would I lessen it’s worth if I polished the silver?

Replacement value around $1200-1500.00 for insurance purposes. At auction on a good day with a knowledgeable collector $600-800.
Yes you can polish it if you use a proper silver polishing cloth… NO CHEMICALS! and do it carefully by hand. It should then be stored in an air tight container to keep it from tarnishing again. I like to us plastic sealable bags. Or as I said, in a ryker frame out of the sunlight where you can see it.
Or just wear it if there is no fraying showing anywhere. It’s a beautiful old piece that just isn’t made anymore because of the work involved and the rarity of old untreated coral.
Look on the top of the collars and the cones to see if there is a signature, that always increases the price.