Forget about care vs. no care- this concerns me in a different light:
What if the Teen and her parents don't agree about what should be done about the pregnancy???? Who gets the choice then?
What if the parents are against abortion so they wont sign the paperwork even though the teen wants (and understands and agrees) to one.
Or what if the parents want their teen to get an abortion and she doesn't want one... The parents could technically sign off on it and it gives no right to the teen...
I haven't read the law but THIS is a bigger issue then care vs no care-
Well in a case in which the teen wants the abortion and the parent wants to force her to remain pregnant, the parent wins no question in the states with consent laws (as far as I know at least).

I can only assume this is exactly what politicians and pro-life groups were banking on when they passed the law--that many parents would stop their teens from aborting. (I certainly have no doubt that the consent laws would have passed if politicians and pro-life groups thought that many parents would actually force their daughters to have abortions.)
I don't know what happens when the parent wants to force an unwilling teen to have an abortion. Legally if they can force her to be pregnant, it only follows that they should be allowed to force her to have the abortion as well.
I was actually wondering since everyone is making so much of parental authority, what about the teen's parental authority over her fetus? Or for that matter, what about a 17 year old who has birthed a child? I assume a 17 year old mother can be the legal guardian of her own child? (I've never heard otherwise at least.) So imagine a case 9 months into a pregnancy in which the pregnant 17 teen year old's unborn baby will die unless she has a c-section. Do the parents of the teen have the legal parental authority to refuse to allow her to have the c-section, thus causing her baby's death? And if so, doesn't this violate the teen's legal parental authority?
Personally I think that regarding ALL medical procedure that requires parental consent, there should be a system of judicial bypass in which an older child can overrule the parents. I know sometimes teens are granted the right to make their own medical decisions in some cases. And regarding abortion states which require parental consent for abortion are constitutionally required to have a judicial bypass procedure (which the parents never know about). Unfortunately these systems are largely a joke. A professor of mine did research on the Pennsylvania system and found 2/3 of the courthouses in the county were completely unprepared to deal with a judicial bypass. Most didn't know what it even was. Some had no judges willing to even hear the request since it involved abortion. And sometimes the person requesting the bypass couldn't get past the receptionist who told her how abortion is murder.
I tend to be suspicious of the movement to add laws to the books to protect parental authority to force their teenagers to do or not do certain things regarding their reproductive health. My mother was always very in favor of such laws; she always said, "Well if you were having an abortion, I'd want to know about it." I always thought, "Well if you wanted me to tell you that I was going to have an abortion, all you had to do was encourage an open atmosphere where we could talk about sex and where I'd know that you'd support me in any reproductive decision I make in the chance of an unplanned pregnancy." But my mother didn't really do that when I was a teen, so I likely would not have told her about getting an abortion. A law that forced me to do so would just have sent me to the next state over.