No they do not, the recipient however pays a fee of $1.49 to retrieve the letter that the inmate sent to you, through InmateAid.
https://www.inmateaid.com/ask-the-inmate/when-an-inmate-responds-to-an-inmate-aid-letter-do-they-have-to-pay-to-use-the-service#answer
Accepted Answer Date Created: July 04,2018