I think that a large quilt will help in the same way that curtains help. I removed the carpeting in my living/dining room once and had the hardwood floors underneath refinished, and it took me weeks to get used to the new sounds in the house - everything echoed. I realize the area of the carpet is much larger than a quilt, but every bit helps.

Maybe the person could put up something really good for soundproofing and have it hidden behind the quilt.

Sorry, I have no advice on the best kind of batting. Probably whatever is the most dense.

I have experience with this. When I was a middle school librarian back at the beginning of computer integration into schools, the "powers that be" decided to whack off a corner of the library for our first computer lab. That meant lots of traffic and noisy middle schoolers. I loved them dearly and wasn't a "quiet" librarian, but something had to be done. So my students made tied quilts! Lots of them! They covered the walls of the lab and they really did work nicely. I am sure that we used the cheapest poly batting available and they were tied. Can't get more basic than that! Plus the kids loved their work on display. Yes, back then, I taught the computer classes and ran the lab too. Of course, librarians had nothing much else to do back then! LOL!

PS. I got my cataloging caught up only twice in 25 years! I was also the computer network administrator for the school.

This is a great idea! Get some of that sound-proofing egg carton foam they use in recording studios, and hang it behind the quilt.

ETA: Ok gang I just asked my husband. He makes high-end speakers, and uses batting inside the speakers. Originally I was asking him what kind of batting is best, but once he figured out what the conversation was about, he said the OP should use Rockwool. It's a sound-proofing material they use in commercial buildings. Here's one of many YouTube videos that show how to use it.

https://www.youtube.com/watch?v=YnN-AttTyoc

Here's another, more detailed how-to video: https://www.youtube.com/watch?v=tLk6fQVcoSw

You could easily cover it with decorative fabric or a quilt top, or just make the panel and hang the quilt in front of it.