Paul was once a "leper" to Christians, a vicious persecutor of those who followed Jesus. He was converted but the community didn't believe it, and wouldn't allow Paul into the circle of Christians. Barnabas was convinced of Paul's genuine, authentic conversion and persuaded the community. The best way Paul could give evidence of his healing from "leprosy" was to produce good fruit and so glorify God (Jn 15:8).
Mark was a "leper" in that he deserted the first Christian missionary journey (Acts 13:13; 15:38). Barnabas gave Mark another chance. While Paul refused to believe that Mark was genuinely healed and ready to evangelize again, Barnabas believed in Mark. The best way Mark could give evidence of his healing was to produce good fruit and so glorify God (Jn 15:8).
Healed and converted "lepers" are accountable to God, not man. They need not prove themselves before men. However, some people need evidence of full conversion and healing (see Mt 3:8), and the best evidence is fruit (Mt 7:20), that is, undeniable holiness and good works for His kingdom.
All disciples of Jesus are preoccupied with bearing fruit for Him. If we just concentrate on bearing fruit for Jesus, God will make sure that everything else we need is taken care of. "Go forth and bear fruit" (Jn 15:16).