Pietersen hopes to join the team for the four-Test tour of India in November after publicly apologising for his row with the ECB and signing a new four-month contract.
Strauss said the true test will come when Pietersen mixes with teammates behind closed doors, The Sun reports.
He said: "In terms of the cricket, the important thing is what happens in the dressing room and how Kevin and the guys deal with what has gone on. That's the acid test, because if that side of things is not right then the team won't play well going forward.
"If people can get that process done properly and don't leave anything unsaid, England will go from strength to strength. If not, that will be more of a challenge."
Strauss insists England can only benefit if Pietersen and the team can rebuild a mutual respect.
He added: "The best-case scenario is the best batsman in the side is back, the environment is happy and everyone trusts and respects each other by being united in a common cause. The challenge is to get to that situation and the crucial thing is that everyone genuinely wants it to happen."