Does the husband’s statement after reconciliation, "I only took you back as a mut'ah marriage," constitute a valid form of marriage, and what is the ruling of Islamic law on that, considering that the wife became pregnant and gave birth to a daughter?

If the return (reconciliation) occurs before the expiration of the waiting period (iddah (definition)) of a revocable divorce, then it is considered valid and sound, and the child is attributed to the husband. His statement "temporary marriage" (mut'ah) is not given any consideration due to the absence of its conditions. However, if the return occurs after the expiration of the waiting period and the final separation (bainunah), then it is not considered valid and requires a new contract. The child is attributed to him if he believed in the validity of this return.