This feature unlocks as soon as you awaken your first girl or Pet. It will be shown under "Institute", on the main menu.
Here, you will be able to "purify" the awakening gears, granting certain bonuses to the Battle Girls' and Pets' stats.
The proccess is very simple: Choose an awakened Battle Girl, and the gear will be ready to be purified.
Tap the STR, INT and AGI checkboxes to lock them and to make sure the purification is successful.
Next, tap "Purify" and your current purification value will be raised by one point on the stats you have locked.
By leaving the stats unlocked, the purification values will be randomized, meaning they can either be raised by more than one point or be lowered by several points.
The purification will only be concluded when you tap "Save", so if that happens, you can just go back to the main menu. However, your free purification will still count as used.
The bonuses will only be granted once their caps are reached. The caps' allocation on the stats vary from one gear to the other, but their values will always be 40, 100 and 200.
One free purification will be available every 22 hours. Alternatively, you can perform them at the cost of Gold Coins, Tickets (Can be earned at Lucky Wheel events), or Diamonds, by checking the "Advanced Purify" option.