How does the Treasury General Account Balance control inflation?

The FED controls inflation by removing liquidity from circulation and reducing pressures for banks to add liquidity into circulation.

Arrows marked "created" show when money is debited from the FED thus creating  money and crediting it to accounts in the economy.

Arrows marked "destroyed" show when money is debited from accounts in the economy and credited to the FED thus the money ceases.

The TGA keeps a daily balance of $300 billion, which means that it constantly removes $300 billion more from the economy than it adds to it.

The constant generation and removal of money keeps the money flowing.  When money circulates to someone who saves it, then its value is reduced by interest accumulations when it is loaned out. Eventually it stops circulating due to lack of borrowers. 

Before the FED, banks generated money with regard to who had collateral to stimulate its generation.  When not enough entities were borrowing, economic depressions occured.  When too many entities were borrowing, inflation would soar.

The general Federal Reserve mechanisms to control the flow of money are described here.  The explanation for the large TGA balance is here.