Implies looking for something quickly without being organized.

Hasty Searching

Suggests the person is getting frustrated or desperate while looking.

Impatience Implied

Often used to create a vivid picture of someone rummaging through something.

Refers to animals digging or scraping for food or making a nest.

This action is usually instinctual to animals, as part of their survival.

When you see 'scratch about', it often describes observable animal activity.