The price of btc denominated in tether (BTC-USDT) goes up after our transaction. Now, arbitrage bots will look at this in crease in btc-usdt, and be mandated to buy btc with USD so that BTC-USDT and BTC-USD are in parity. Now bitcoin's price in dollars has gone up and people notice this, and news articles are printed and people get FOMO.
But at the root of this pump is a fraudulent transaction. I printed tether that I know is not worth one dollar each, and you played along with me and we exchanged tether for btc, and we caused btc to go up in price so that we both benefit. Whomever buys btc (i.e. retail investors) after I've pumped the price is in great danger of being scammed because there was no real money behind the initial tether transaction. You, the exchange, might be holding a lot of useless tether, but it doesn't matter because you've already profited from the price increase in btc via higher trade volume and usage of your platform plus all the publicity you get from a media that is always happy to report insane btc valuations.
So you don't do anything with the tether, you don't care about it as the exchange. It's unclear if the tether in these exchanges, which is a lot, will be redeemed for dollars at some point in the future by coming back to me, the Tether company, where I would use some of my profits from selling btc high to trade some of your tether for USD and help maintain the appearance that tether is fully backed by USD.