I requested direct deposit but now I'm being sent a check (which may not reach me until JUNE). Why am I getting a check and why was I not alerted sooner?

The IRS can decide to send you a check instead of making a direct deposit.  Or you may have entered incorrect banking information for your direct deposit.  TurboTax does not receive any information about this to "alert" you, nor does the IRS alert you.

If you entered incorrect banking information for your refund, you can change it if your return is rejected.  If it is accepted, however, it is too late to change it.  The bank will reject the refund and send it back to the IRS.  Then the IRS will issue a paper check and mail it to the address you put on your tax return.  Expect a delay of at least a couple of weeks to receive your refund.

Here is what the IRS says about entering incorrect banking information

https://www.irs.gov/help-resources/tools-faqs/faqs-for-individuals/frequently-asked-tax-questions-answers/irs-procedures/refund-inquiries/refund-inquiries-18