@ DoctorWho asked: "Why has the IRS wrongfully decided they must send us the Federal income tax return using direct deposit? Has the Federal government decreed that the only way they can send Federal Income Tax returns is by using direct deposit?"
Yes, it was a decree as a result of an Executive Order. The IRS and other government agencies are phasing out paper checks. NOTE: There are a small number of exceptions for tax refunds for situations where it can't be sent by direct deposit. Ultimately, they will also phase out paper checks that some taxpayers use to make tax payments as well.
What type of notice did you get--is it a CP53A or CP53E? The below is my understanding, and I am not a tax expert, but a fellow user.
A CP53A is a longstanding notice sent to taxpayers over the years when a bank rejects a direct deposit and sends it back to the IRS. This would tell taxpayers that they will likely be sending a check. A CP53A letter wouldn't seem to apply in your circumstance. You probably got CP53E.
@ xmasbaby0 provided a link above for into about a CP53A notice, but that is not likely the type of notice you got. So if needed, I've provided a CP53E link below.
You probably got the newer CP53E notice, which is sent when the IRS doesn't want to send a check and prefers to use direct deposit instead as required by the Executive Order, but no banking info or incorrect info was provided. So it's essentially informing the taxpayer of the transition to electronic refunds and giving the taxpayer a second chance to choose direct deposit instead of a check. I haven't seen the wording of the letter, but it's probably confusing as is often the case with the IRS.
CP53E Notice
https://www.irs.gov/individuals/understanding-your-cp53e-notice
You asked: "Is there any way I can verify that I asked them to mail me the refund check, so when I call them, I can tell them they got it wrong?"
The IRS already knows what you chose, but they don't want to send paper checks unless they have to. Maybe you fall into one of the exceptions; ask the IRS.
But to see your refund choice, there is a page in the return PDF called "Electronic Filing Instructions" that should show your refund choice. Or that page can be viewed in Forms Mode if you are using desktop TurboTax.