Is the relationship considered marital or adulterous if a man takes back his irrevocably divorced wife (divorce minor, final) verbally only during her waiting period, believing that to be permissible?

If you reconcile with your wife during her 'iddah (definition) (waiting period), she returns to your marital bond without a new contract, mahr (dowry), or witnesses, provided that the 'iddah is a revocable one (i.e., a first or second divorce after consummation or valid seclusion). However, if you divorced her before consummation or valid seclusion, she has no 'iddah, and she is irrevocably separated from you with a minor irrevocable divorce (baynunah sughra). You cannot take her back except with a new contract, a guardian (wali), witnesses, and a mahr. Therefore, if she has been irrevocably separated from you with a minor irrevocable divorce, your reconciliation with her simply by agreement is invalid, and a new contract is required. It is advisable to present the matter to scholars to determine the reason for the irrevocable separation.