Can I change the message shoppers see when they find a Find & Earn gift?

Yes. There are store-wide defaults and per-event overrides.

• Store-wide: go to Plugins → Find & Earn → Settings. Under Default templates, each outcome has an On-screen message and an Email: Gift found (no coupon), Item coupon won, Item coupon limit reached, Completion coupon won, Completion coupon limit reached and Already opened (on-screen only). Click Save settings.
• One event: in Plugins → Find & Earn → Events, click Manage on the event, open Email Messages, tick Override store defaults for this event, edit the text and click Save email messages.

Every event uses the defaults unless it overrides them.