To take into account means to think about or consider someone or something, and in this context the person is considering the assertions made about the ability to parent.
Context: "What I have to do is examine the evidence they have provided and consider your own assertions of your ability to parent." Claim: "What I have to do is examine the evidence they have provided and take into account your own assertions of your ability to parent."
Considering the context, is the claim true, false, or unknown?