The oxidation products of CHP are phenol and acetone, which are intermediates for the preparation of phenol from cumene. So there are many patented methods to remove CHP from phenol, but the reverse is basically not. The packaging should be protected by nitrogen or argon, and the sealing should slow down the oxidation and lead to discoloration. Long-term preservation should be at low temperature, and you may already be doing it.
It should be difficult to remove, even if it is removed, it will degrade into phenol when exposed to air. A small amount of phenol/benzoquinone leads to ugly color, but it should not affect the use.