It doesn't sound like the USD has a ton of exposure here, so how would it bubble up? Does a major bank (Citi, Chase, BofA, etc.) have a large position in Tether?
A recent fear was Tether holding dollar-denominated commercial paper. If they went under, they'd dump that paper. This happened in '08 with money market funds, and we passed a lot of regulation to ensure that failure mode can't happen again.
Fortunately, to the extent Tether holds anything, it isn't cash or U.S. dollar commercial paper. So contagion vector contained.