What does Pearl want from Dimmesdale?

This child of its father's guilt and its mother's shame hath come from the hand of God, to work in many ways upon her heart, who pleads so earnestly, and with such bitterness of spirit, the right to keep her. It was meant for a blessing; for the one blessing of her life! It was meant, doubtless, as the mother herself hath told us, for a retribution too; a torture, to be felt at many an unthought of moment; a pang, a sting, an ever-recurring agony, in the midst of a troubled joy! Hath she not expressed this thought in the garb of the poor child, so forcibly reminding us of that red symbol which sears her bosom?"