No, you response is also Giftwrapped DM

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What’s the warning for then?

Warning for: Your friends are not using Client’s Support Giftwrapped DM and may not be able to receive your Giftwrapped messages.

Is there an option to send an unwrapped message to make sure they get it?

Unfortunately, it's no longer available to prevent users from accidentally sending an unwrapped DM. Perhaps you could use another client to notify the other person

Wow, thanks for the information