Is it possible for someone not a lawyer because of financial reasons get a Quit Claim reversed and signed back to estate due to the signing done while the person was mentally incompetent? We have been told that the person who signed the quit claim deed was found as such four days before he died. But we are unable to get a copy of this because we were not listed as contacts.
Or do we just try ourselves to do a reversal?

To get a copy of the Quit Claim Deed go down to the Recorder's Office and speak with them to get a copy. It's public information available to anyone who asks and has a copying fee in their hand.

... We have been told that the person who signed the quit claim deed was found [to be mentally incompetent] four days before he died. ...

How long was it before he died that he signed the deed?

Is it possible [to]... get a Quit Claim reversed ....
Or do we just try ourselves to do a reversal?

The term would be "declared void". What interest do you have in the matter? Are you an heir?

First it is not going to happen without an attorney, this is going to be a very involved. You are going to have to get medical doctors to testify in court that the person who signed the deed was not of sound mind at the time.