Thank you for using justanswer.Different expert here.
Unfortunately, the expert above is correct (please see below)
I am however, a little surprised that you bank didn't recognize the error, since you had your complete account #, (it shouldn't have that hard to figure out that the last numbers were a check number.)
You can try calling the IRS at 800-829-1040, and if they haven't already sent out the check , you MIGHT be able to get them to send it through again, (however, this is a REALLY long shot) and then let your bank know what you did, and ask them if they could keep an eye out for it and go ahead and deposit it for you.
In all probability though, your refund will end up coming by mail.
I'm sincerely sorry that this happened. I know how frustrating this is. However, it sounds like this happened just a little while ago, while IRS was winding down from the tax
year, and that may work in your favor, since they're nearly as swamped now and the would have been earlier in the tax year.
I know this is not the answer you want, but I hope it at least gives you some clarity on this subject.