Federal Inmate Record

What happens if you send a letter to someone in jail?

If I send a letter to someone in prison, they keep a record of it, of all people who exchange letters with federal inmates.
But, what do they do with it? Like, if you wanna get a visa to travel to the US, would that be a issue? What are the consequences of being on that list?
And im talking about harmless letters

All letters will be vetted