A big thank for explaining about Zigner, I got it now.
The lease has this condition:
No amendment, alteration, addition, or change to this lease shall be binding on Tenant or Landlord, unless reduced to writing and signed by them and by direct reference made a part hereof
But the agreement I recently signed with the husband alone for rental reduction, in exchange for the repair costs I paid, does not state that the agreement is (or will be) part of the lease (or intended to be part of the lease) or anything like that (FYI, the word “part” is not there in the agreement). This may make that agreement not binding on Landlord (wife and husband).