Is it true that the Treasury issues an I.O.U. to the Federal reserve every time they print more money?

No.

The government borrows money by issuing U.S. Treasury securities which are then sold at auction. Anyone may buy these securities at this auction, even you. However, by law, the Federal Reserve is prohibited from buying U.S. Treasury securities at these auctions. The Federal Reserve buys the U.S. Treasury securities that it holds on the open market. The open market is where previous purchasers of the securities sell them before the maturity date of the security.

How does the Federal Reserve pay for those securities? It simply creates money. Whenever the Fed decides to buy securities on the open market, it gets bids from brokers on the particular amount of securities that it wants to buy. Once a bid is accepted, the broker delivers the securities to the Fed and the Fed increases the account of the broker's bank at one of the Federal Reserve district banks. This is done through a simple accounting entry. No physical money is printed or exchanged at this point.

The printing of money is performed by the U.S. Treasury. The Federal Reserve pays the U.S. Treasury an amount that reimburses the Treasury for the cost of printing the bills. The Federal Reserve has to pledge as collateral the U.S. Treasury securities or other assets for any new bills that are not replacing existing bills. The new bills that are not replacing existing bills do not enter into circulation until they are withdrawn from the Federal Reserve district bank by one of the member banks. Typically, a member bank would withdraw from its account at the Federal Reserve district bank and would take delivery of printed bills if it needs to.

As for the mortgages, the media, talking heads, and people in general, tend to exaggerate when discussing mortgage backed securities. In simple terms, banks can only lend out money as long as it doesn't exceed 90% of deposits. Once a bank has reached that limit, it cannot make any additional loans unless a previous loan is repaid, it gets more depositors, or it can sell existing loans to an investor or another bank. Once a bank has sold the mortgages in a security, it can continue to make additional mortgage loans because the other mortgages no longer belong to it.

Mortgage backed securities took a lot of flak during the financial crisis, but that was mainly because people didn't understand them. What happened was some securities had a higher than average amount of mortgages that were expected to default. So, when the mortgage crisis happened, the market for mortgage backed securities came to a halt temporarily. Mortgage backed securities are required to be accounted for as mark-to-market, which means that when the market disappeared or slowed, the recorded value of those securities was required to be essentially zero. That doesn't mean that all the mortgages in those securities were going to default or be bad. It was just a requirement under accounting rules. However, that caused the balance sheets of some very big banks and investment firms to fluctuate drastically.

Even though I have said all of the above in an attempt to explain it all in layman's terms, you should understand that the mortgage backed securities that the Fed has purchased are similar, yet different. During the financial crisis, many mortgage backed securities held by some of the big banks and investment firms had mortgage failure rates of approximately 8%. In other words, if a security contained 100 mortgages, approximately 8 of them defaulted or were expected to default. The mortgage securities purchased by the Fed have a much lower failure rate of 3 to 4%. In addition, unlike a standard bank, the Fed is capable of holding those securities until they mature regardless of the market value.

I hope that I explained it so you can understand it better. This is all a very complicated subject which is compounded by the fact that there is a lot of nonsense floating around the Internet written by people who don't know WTF they are talking about.

Clearly, others don't understand what the Federal Reserve Bank is. Sure, the Bureau of Engraving prints the physical notes, but those notes are created from thin air, backed with nothing, at interest, for the Federal Reserve Bank cartel. That's why they say "Federal Reserve Note". We cannot print our own counterfeit money, because Woodrow Wilson gave exclusive rights to the private Federal Reserve Bank cartel with the Federal Reserve Act of 1913. Only the cartel can create counterfeit money.

The Federal Reserve System ("The Fed") may purchase any security for any price. It does buy U.S. Treasury bonds -- bonds are issued by the Treasury to borrow money because the federal government spends more than it takes in in taxes.

To pay for the securities the Fed purchases, it creates money - this is called inflating the currency (amount), or just simply "inflation" or "quantitative easing". This new money is created in the form of book entries in Federal Reserve accounts. The Treasury account at the Fed is credited with new money in exchange for Treasury I.O.U.s.

Something like that.