Is a new marriage contract required to return after an irrevocable divorce of lesser degree (طلاق بائن بينونة صغرى), or is it permissible to reconcile without the need for a contract?

The valid privacy [khalwa sahīha] takes the place of consummation [dukhūl], and therefore, it is permissible for the husband to take his wife back without a new contract. Divorce is the last resort for marital problems.