Is it permissible to renew the marriage contract after the husband takes back his divorced wife, before consummation, who became pregnant by him, without the woman observing the 'iddah?

If a man divorces his wife before consummating the marriage, he has no right of return to her. He must separate from her because she is a stranger to him, and her 'iddah (waiting period) from him is until she gives birth. He may contract a new marriage with her if they both desire it, even if she is pregnant, and this pregnancy will be attributed to him because he had believed that the marriage between them was still valid.