I receive a visit from the mascot every time I load a game that has eligible Sims in the household. I just pause, find out the mascot's name, and use the ResetSim cheat to send him away.
The baskets can be sold. Or, for that matter, bought - so don't worry that you're sacrificing your chance to take the aptitude test by selling the kits, if you decide to go to University some day.