If my tax return has been rejected and I need to file it by mail, do I need to send a check with the return to pay the taxes? I had authorized echeck on TurboTax.

You could do that, or better yet you can pay electronically at the IRS Pay site.

irs.gov/pay

That way you can save the stamp and avoid a trip to the post office, plus you get confirmation that you paid. WIth the COVID-19 shutdown earlier this year, the IRS is way backlogged on paper returns and they might not get around to processing the check payment for a long time.