This situation calls for courage, wisdom and tact. The most important thing I can say is not to go forward on your own. As the Sunday School teacher, you only see and hear one side of the story. Your first step should be to go and talk with someone you respect in church leadership. This could be an elder, a pastor, a deacon, or someone else. The fact that this couple also leads a Bible study makes it more challenging.
Go to that trusted leader, tell them what you have seen and heard and ask for their advice. It may be that the child is given to exaggeration. It may be that things are not as bad as you fear. By going to a trusted leader, you can share your concerns and ask for help.
I would not advise you to go to the parents on your own, alone, because of the delicacy of the issues involved. No matter your motives, it is very easy to be misunderstood. This is a time to act in concert with others. You need the wisdom that others can bring who are not as involved as you are.
Having said that, you are right to be concerned. Now trust that your leadership will help you know how to proceed from here.