As you may know (from IDEX faq):
How do you safeguard my private key?
When a user unlocks their wallet, their private key is stored encrypted in browser memory and cannot be accessed outside of the IDEX app. Private keys are only accessed locally to sign transactions on behalf of a user and are never transmitted outside the device. On sign out, the private key is destroyed from memory and cannot be accessed.
This means that you should have unlocked your wallet before to use IDEX and that the private key is hold by the browser cache, but unfortunately this do not means that it is available in a readable format. The only people who know how it is represented in the browser are those from IDEX, but they specified that it is maintained crypted in the browser and this means that you should know “how it is crypted” as well.
It seems very hard to recover. Anyway it is clear that they are discussing of the private key of your wallet, that may be you can recover from it (depending on the wallet you have).