「ご質問の際は例文を記載されたく。」 This is omission of 「ご質問の際は例文を記載されたくお願い致します」. "れたく" shows request.

As Haru-san said, it would be better if you write some example sentence. However, I'll try to explain about it. It is passive voice + negative form of -たい. Ex.) きかれたくない (I don't want to be heard) きく + られる + -たい + ない いわれたくない (I don't want to be said) いう + られる + -たい + ない I hope this helps you.

I think it would be better to give some examples using this.