I assume you got the job in 2017 and was signed up for the HSA for that same tax year.
First, lets determine if your parents do "in fact" qualify to claim you as a dependent on their tax return. They may not. If you were at least 24 years old on Dec 31 of the tax year, then your parent's do not qualify to claim you on their tax return if you earned more than $4,050 in 2017. Does this apply to you? It probably does not. But we have to confirm so we don't waste time providing information based on incorrect assumptions.