This may not be helpful, and don't hold me to account if your legs fall off or something, but every time I taper I get a whole range of niggles, and the most common is a pain behind my knee-cap. I doubt strengthening exercises would have much of an effect in the time-frame, so as long as it's not affecting your running, I'd probably put it down to taper-madness.
If you are worried it might be worth seeing a physio - that's my disclaimer.