According to the Ben 10 Wiki, 16-year-old Ben regains access to Feedback during the events of Showdown: Part 2:
Suddenly, Ben, in the form of Feedback, emerges from Malware's head. Malware is shocked, but says that he will destroy Feedback again.
It's unclear to both me and the Wiki how 16-year-old Ben was able to do this:
[Feedback] is one of the four regular aliens to be temporarily destroyed and removed from the original Omnitrix/Ultimatrix [...] While Ben has been able to regain the other aliens, it remains unclear as to how he was able to regain Feedback.
~Ben 10 Wiki's page on Feedback (emphasis mine)
What is clear is that, following the events of the Showdown two-parter, 11-year-old Ben can no longer use Feedback, but 16-year-old Ben can. While Store 23 aired before the Showdown two-parter in the US, its events actually takes place afterwards, explaining how 16-year-old Ben is about to use Feedback.
I realise this may not be the most satisfying answer, but it honestly appears that there is no canon explanation for how Ben was able to regain use of Feedback.