How does Gerald see his relationship with Sheila at the end of the play?

At the end of the play, when Gerald makes a call and finds out that Eva Smith has not died and that there has been no case of anyone drinking disinfectant, he is relieved and ebullient. He wants a drink and sides with Mr. Birling in thinking that now everything is all right and can go back to the way it was before the inspector called.
For Sheila, however, it is a different story. As she says, whether Eva committed suicide or not, everything spoken of about her really did happen. She did get fired by Sheila's father from his plant for being an "agitator"; Sheila did get her fired from the department store because she was jealous of her; Gerard really did have an affair with her when he was supposedly courting Sheila; Eric really did rape and impregnate her; and Mrs. Birling really did coldly refuse her request for help. Sheila really did suffer hunger and want. That, says Sheila, she "can't forget." Even though Eva's story apparently didn't end badly, "it might have done."
Gerard wants to go on as if nothing happened. He says to Sheila, "Everything's alright now," and tries to give her back the engagement ring. But Sheila has been shaken and transformed by all she has heard and says:

It's too soon. I must think.

Gerald, unlike Sheila, is too quick to take the easy way out. The lesson of Eva's suffering has not taken hold for him. Once he is out of danger of being blamed for her death, he no longer thinks about her at all. He is completely ready to pick up again with Sheila as if nothing happened.

Gerald thinks that nothing much has really changed in his relationship with Sheila. Yet he's deluding himself. He may not have changed, alright, but things between him and Sheila most certainly have. Although genuinely moved by the death of Alice Renton (a.k.a. Eva Smith), he cannot emerge beneath the shadow of his domineering father. He knows that without his father's money he simply won't be able to make it on his own.
Whatever pangs of conscience Gerald may have felt at Alice's tragic death appear to have vanished by act 3. Because now, Gerald plays the leading role in trying to expose Inspector Goole as an impostor. But Sheila, unlike her fiance, has developed an enduring social conscience; she no longer looks at the world in quite the same way. It's no surprise, then, that she seriously considers returning Gerald's engagement ring. Our abiding impression at the end of the play is that this is not a relationship fated to endure.