Answer:
"Group Home" is not a precise term; it can have several meanings. This answer assumes group home refers to a youth facility that teens are assigned to rather than being placed in juvenile detention or jail.
The Supreme Court has held consistently that prisoners lose some First Amendment rights when they are held. Any form of speech that constitutes a possible threat to security or safety is generally banned, while other freedoms are not supposed to be limited. Jail keepers have wide discretion in saying that talk of (for example) violence, drugs, escape, future plans for crimes, association with gangs, etc., is prohibited.