There should be no problem with them doing the exercise unless they start to notice tendonitis symptoms. That would be tennis elbow type pains or wrist problems. Since this exercise is not dealing with heavy weight resistant training, it is not a problem like a child going in and trying to do heavy weight training.
Focus on the core "BALANCE" strength of the movements of the sport. Not the ability to lift a weight over ones head. The Gripstik is a great tool for kids to develop the user groups (primary and secondary) firing skills of the extensors and flexors. You cannot over train them with the Gripstik, more is better. THe problem with STRENGTH training more times than not, the person lifting the weight is lifting wrong and training the neuromuscular firing response improperly. That takes a long time to retrain in itself. More times it slows the athlete down rather than speeding them up. Much like a work horse showing up at the Kentucky Derby expecting to win.
Moms and Dads: This might be a great time to instill the concept of "perfect practice" Review the instructions with them, monitor their technique, and encourage a high rep, lower resistance training where they are first developing the range of motion and flexibility. From there, they can slowly increase the resistance. Once again, a 15 second target time is recommended for children to start with.