1) Click on the circled icon, click to claim the rewards.
2) They will appear in your mailbox. Claim them from the mailbox.
3) A window will pop up asking if you want to open them now. Click yes.
4) It will take you to the items tab, where you can then select a character and how many elephs you want to claim.
5) Since you've been playing for a few days now, close the Special mission event window and check it again after 5 minutes, to see if you can retroactively claim the rewards from previous days.