I know History.com is not a good source, but this claim is mentioned on wikipedia and frequently mentioned elsewhere and touted as fact, but I’ve been strugling to find any evidence for it.

As mentioned here in this article

«The boatlift also began to have negative political implications for U.S. President Jimmy Carter. When it was discovered that a number of the exiles had been released from Cuban jails and mental health facilities, many were placed in refugee camps while others were held in federal prisons to undergo deportation hearings. Of the 125,000 “Marielitos,” as the refugees came to be known, who landed in Florida, more than 1,700 were jailed and another 587 were detained until they could find sponsors.»

If I’m not misremembering, I read that Castro in 1978 told political prisoners and Cubans in exile that they could go to the US, but other than that nothing in relation to the post question.