IANAL, and I would be eager to listen to someone who has legal experience with research funding, fellowships, universities...but I am familiar with situations at universities and funding as similar things have happened to me.

First if your fellowship is considered a "grant" I've only heard of schools taking overhead from the total award not just research money or the leftovers.

Can you simply just not TA (do an RAship) and make it work with your fellowship funding as is? Or is your tuition much much greater than the 11k? Can the leftover money cover tuition?

If not, is it instead possible, for them to reclassify you as an "hourly" RA? I find that is one way to get around some of these issues with RA wage caps.

I am also concerned about your TAship being supplemented by fellowship funding. Fellowship funding is for your research not to support teaching pursuits (unless its a special fellowship). I will contact the Program Officer again on the phone.

It would be helpful if you could review the terms of your fellowship in detail because some fellowships indeed can be taxed and have indirect costs removed if they go through the university while others like NSF's that u/guruwin mentioned go directly to the person (who is then responsible for taxes).

IF they go through the university, then I've found other limitations are applied. In my case, I was a TA with a very modest stipend with tuition waiver (from TAing). I also had a modest research fellowship that could not cover both tuition, research, and stipend. Because I now had an external source of funding, however, the university had to pay 50% of the tuition from my fellowship funds and use only 50% from the TAship. From that rule, I incurred about 6k in unexpected costs from my fellowship budget.

I wonder if something similar is happening to you?