My parents want to keep my mahr. Whose right is the mahr really?

The mahr is entirely your right as the wife, not the right of your parents, your wali or your husband. Your parents may mean well, for example wanting to keep it safe for your future. If you are willing, there is nothing wrong with giving it to them or entrusting it to them. But the decision is yours. Say it gently: ‘Thank you, Mum and Dad, for wanting to look after it. I plan to keep it myself in a savings account.’ If you want to help them, give part of it as a gift willingly. That way love is preserved and your right stays clear. See mahr (dower).