When you purchase Savings Bonds with your refund, the information is transmitted to the IRS, and they process the purchasing of the bonds.
Per the IRS Using Your Income Tax Refund to Save by Buying U.S. Savings Bonds webpage:
Your savings bonds are ordered after the IRS completes processing your tax return. Once ordered, it may take up to three weeks for your savings bonds to arrive in the mail. If you’re having a portion of your refund deposited directly into your bank account, you may receive your refund before your savings bonds arrive by mail.
If you make an error that increases your refund, the additional amount will be sent to you in the form of a check. If your error results in a decreased refund, the entire refund will be sent to you in a check.
The first step is to check the status of your refund by going to the "Where's My Refund" feature on www.irs.gov or calling 1-800-829-1954. You can generally get information about your refund 72 hours after the IRS acknowledges receipt of your e-filed return, or three to four weeks after mailing a paper return. If the IRS has processed your refund and placed the order for your savings bonds, you will need to contact Treasury Retail Securities Services at 844-284-2676 to inquire about the status of your savings bonds.
Go to the IRS Now you can buy U.S. Series I Savings Bonds for anyone with your tax refund webpage for more information.
Note that any link in the information above is updated each year automatically and will take you to the most recent version of the webpage or document at the time it is accessed.