What is the ruling regarding a woman remaining with her husband who uttered words that may be considered disbelieving, and is renewing the marriage contract necessary in this case?

The phrases mentioned do not indicate the husband's disbelief (kufr). If an utterance that appears to be disbelief can be interpreted in a way that does not signify disbelief, even if that interpretation is remote, the speaker is not considered a disbeliever. Scholars have stated that if there are ninety-nine reasons to declare a Muslim a disbeliever, and one reason to keep him within Islam, then one should act upon the latter reason; based on the Prophet's (peace be upon him) saying: "Avert the prescribed punishments from Muslims as much as you can."