Yes, the young people who were trying to 'improve' the carving should be punished with jail time. Vandalism is an offence that often results in jail time, and what these young people did was vandalism. Their intention, especially with something linked to an ancient culture, should not matter; they should be punished in a way that imposes upon them how severe the crime was.
Damaging an ancient rock carving is a crime and those guilty of the crime should be punished by spending time in jail. The claim of the youths in Norway they they were simply trying to "improve" the carving is preposterous, shows a complete lack of respect and should be rejected. The historical carving can never be returned to its original condition because of this thoughtless crime and those committing the crime deserve jail time.
Trying to "improve" a work of art or an ancient wonder isn't an excuse. I can't go into the Louvre and draw eyebrows on the Mona Lisa and argue that da Vinci made a mistake by forgetting them. The "improve" excuse means they were aware of the significance of the rock carving and felt they deserved to do whatever they want. Some jail time and community service seems fair.
The youths that damaged a 5,000 year old rock carving in Norway should not face jail time. There is no evidence this was done maliciously, and the youths claims they were trying to improve it. Although misguided, this should not rise to the level of a criminal offense. Instead, the youths should have to pay steep fines and be part of the team that tries to fix the rock.