The paws only symbolize a completion of each day. You will receive a paw with 3 red jewels if you solve it on the first day of the release of the game.  For instance if you solved today's deal, you will see 3 red jewels in the paw.  If you solve yesterdays game today, you will get a paw with no jewels.  There is no significance other than that.  

 

You do not get extra points for solving a daily deal on that day, every day is counted as 1 day.  You get a point or a paw point for each day you solve and that is working toward getting a bronze, silver or gold paw for the month.  10 days completed you get a bronze, 20 days silver or full month gold cup.