Is it permissible to speak with a former husband after the 'iddah period has ended if he asks to return and wants to keep the matter a secret from his family?

The completion of the 'iddah (definition) (waiting period) terminates the marital relationship, making the husband a stranger [to his ex-wife], and it is not permissible for them to speak to each other [in a familiar manner]. If they wish to reconcile, they must renew the marriage contract in the presence of the wife's guardian (wali) or his representative, with two witnesses, a dowry (mahr), and the صيغة عقد (formula of contract). If the guardian refuses without a legitimate شرعي reason, the matter can be referred to a judge.