If the teen girl was already covered under her parents' health insurance, she would continue to be covered after giving birth. It might be difficult to add her to their insurance after the child is born, but any teen child who still lives at home can be covered under their parents' health insurance plans so long as they meet other qualifications. It should be noted, however, that adding a pregnant girl may not include coverage for prenatal care and childbirth, as many policies consider pregnancy to be an existing condition and will not cover it.
Assuming the teen was already covered under the health plan before she became pregnant, her prenatal care and delivery would be covered under most health insurance policies. The problem she would face is that the newborn child would not qualify for coverage under the grandparent's policy, and would require some form of insurance in addition to the mother's coverage.
If the girl qualifies, she may be able to get government assistance for herself and the coming child. This type of coverage is available to persons with low incomes, disabilities, and other reasons. It is generally applied for through Medicaid or the local Family Services office. This would cover the prenatal and childbirth costs, and provide for necessary coverage until such time as the young mother was able to secure regular health insurance coverage.