It is evident that the parents are concerned about Mathilda.  The doctor's initial impressions of them confirm as much:  "I could see that they were all very nervous, eyeing me up and down distrustfully."  The nervousness of the parents reflects a certain fear about why their child is sick.  This would reflect that they have a caring attitude toward her. In the initial stages of the struggle, this becomes clear as the parents do their best to plead with the child to let the doctor examine her throat.  The mother's insistence of the doctor being "a nice man" and the father's "dread of hurting her" also conveys how they have an overall caring attitude towards her.

The parents are ineffective in being able to reach Mathilda.  Perhaps, this is out of fear of stepping outside of their own comfort zone or out of sincere fear in not knowing what is wrong with their child.  Their ineffectiveness might also help to explain why the child is so intensely driven to not let the doctor see inside her mouth and throat.  In the end, the parents' attitudes towards Mathilda are secondary to the intense battle that the child and doctor wage, making them more of bystanders than anything else.