Is it permissible to market 'Umrah programs through banks with monthly installments without burdening the pilgrim with any bank interest? And if it is not permissible, what is the ideal way to implement such programs?

There is no obligation to seek out funds for 'Umrah or Hajj, nor to borrow for this purpose. Rather, Hajj and 'Umrah are obligatory upon whoever possesses wealth exceeding their basic expenses and the expenses of those they support, and who is physically capable. It is permissible to borrow for Hajj or 'Umrah if the borrower knows they are capable of repayment, and there is no harm in taking a good loan (Qard Hasan) without interest from any party.