Can Decree of Strength choose Rebuttal (Mel's Signature Spell)?

Yes, Decree of Strength can choose Rebuttal.

Decree of Strength says: "Choose an opponent. They reveal their hand and you choose a Mind ([C]) card from it." Rebuttal's domains are Mind and Chaos. A card qualifies as "a Mind card" if it has the Mind domain — it doesn't need to be only Mind. Rebuttal is a Mind card and can be chosen from the revealed hand and recycled, regardless of its Chaos domain or Signature status.