It's really very simple. Tether is meant to be designed such that you can buy 1 "tether" (USDT) for $1 and sell for $1, initially the suggestion was that every tether in existence was backed by $1 in a bank account owned by the issuer. But that doesn't seem to be true. So how do you manipulate BTC using USDT? You just print USDT and use them to buy BTC. Everyone thinks that 1 USDT = $1, so they're willing to receive it. As long as no one actually tries to cash out the USDT, it's fine. And why would you cash out? Bitcoin is going to the moon!

So as long as there's a net inflow of cash into tether, the issuer of tether can just pump the market up using unbacked USDT.