That's a complete distortion of what's actually happening. If this were actually happening and people knew about it there would be absolute outrage.

The truth is that Citadel is one of a few firms that pay Robinhood for the option to take the other side of trades. It's pretty innocuous but people get upset about it and turn it into "Citadel get advance knowledge of Robinhood trades".

Citadel is in the business of making markets. Instead of taking a position on a stock, they just happily take the other side of most trades. They make their money by offering slightly below the "true" market price and in exchange they provide liquidity to the market so that you can sell your stock pretty much whenever you want. The idea is that most trades are pretty random and for each trade on one side you have a trade on the other side that balances it out and Citadel keeps the difference between the "true" price and what they pay/sell at.

The problem is that sometimes lots of stock will be sold for a good reason (imagine someone finds out that there's an accounting fraud at some company). In this case, Citadel loses money because the trades don't balance out and the stock just goes down.

From Citadel's perspective, traders on Robinhood are much more likely to be random people with no extra info (retail investors) and so they're willing to pay Robinhood to route the orders to them because it reduces the risk of adverse selection. In exchange, Citadel has to give a price that's at least equal to the best price in the market or else they're not allowed to fulfill the order.