Possible Clues:

• Small squirrel
• Burrowing squirrel with cheek pouches
• Member of the squirrel family
• Bit of wood? One found in order, we hear, for rodent
• Animal
• Alvin is one, so is Theodore
• American creature caught greeting quietly spoken brother
• Beastly assistant to the fish friar, say?
• Squirrel's lunchtime - tucked into hearty portion
• The little beast sounds like a friar in a monastery