Take the tube off and see if the peep stays aligned when the bow is drawn.
If it doesn't (and probably won't) you can always buy a (Shurz a Peep).
Your present peep is probably installed by splitting the bow string in half whereas the 'Shurz a Peep' is designed to be installed by splitting the bow string strands into thirds.
If the 'Shurz a Peep' doesn't align when the bow is drawn you can move an individual strand on the bow string from one notch to another on the peep to pull the peep sight around and make it line up better.
There should be instructions on installing and adjusting it included if you buy one.
Shurz a peep pic -
