Power strips either work or not.
It should only affect the device in that it may or may not get a charge.
Is the power strip also a surge protector?
If so, the surge protection has a set lifespan.
Once it cannot absorb any more surges, it will no longer do so.
On a modern surge suppressor power strip, once the surge suppressor has reached its limit, then no more power will be provided to the power strip.
On an old surge suppressor power strip, power may continue to be provided even after the surge suppressor no longer works.
Surge suppression is best for sensitive electronics, and power strips without it are fine for power tools and intermittant large draw items (they make surges of their own).
Most modern power grids are well adapted and do not have the surge problems of years ago, but there are other things that can cause issues where surge suppression may be desireable.
If the function of a power strip of either type is in doubt, I replace it.
They literally can be had for a couple or a few bucks at most any store.
Modern products are cheaply made and are basically disposable, unless you want to pay an exorbitant amount for some industrial grade or professional equipment.
I recently spent $30 on a very nice power strip at Harbor Freight.
I use it at work, it is steel contruction, has two USB ports for charging devices, and attaches to my tool box with strong magnets.
Honestly, I do not even know if it has any surge protection at all.
My guess is that if there is, it resides inside the USB port power conversion area.
Your device has a number of protections against 'bad power', and most likely is in no real danger.
But, electricity can be fickle.
Fluctuating/surging power could cause shortening of the lifespan of the charger for the device.
What exactly is the power strip doing that could be a problem?