I would tell them that they are wrong that the Old is not used, or that it is completely discounted by the new.What would you say to a response from another Christian with tattoos who says The Old Testament isn't used anymore?
Most of Christ's teachings come from the Old Testament, so anyone who follows the new is following at least some wisdoms and rules from the old. This subject is another debate entirely.
I would also tell them, and anyone who wants to have tattoos on their body that it is dangerous for the body, not only is it mutilation of their temple, it's leaving incredible amounts of toxic chemicals and industrialized dyes unnatural to the body inside the largest organ.
If the Israelites were strong enough to remember their dead in prayer, so too can Christians, and so too can they venerate their Lord without depreciating their body for worldly reasons. If the soul is strong enough, then we don't need "reminders" of our dead family members or our favorite Bible verses on ourselves.
I've seen people who call themselves Christian covered with tats, I am not one to judge their redemption but there is a degree of cleansing one should do to all worldly things to get close to Christ. The right ones endure the cost and the pain to remove them because they've spiritually realized they are wrong.