Demurrers are rarely permitted in unlawful detainer actions, and would not be appropriate for the circumstances you described in your question. Consult an unlawful detainer attorney to see if a motion to quash service of summons could be filed. A demurrer only tests the sufficiency of the allegations, not the truth nor can the court consider extrinsic evidence.
Most UD courts don't allow demurrers. Even if they do, demurrers don't challenge the terms that the plaintiff pleaded, which are assumed to be true, even if they're not.
As for trying the case on its merits, you're oral arrangement may not be eforceable. Do you have a written rental agreement that says that rent is due on the 1st of each month with 5 days grace, or on the 5th with no grace days? Does it say something like "no oral agreements or promises, either prior to or contemporaneous with this agreement, may vary the terms in this agreement"? and/or "this written agreement may not be modified or amended except by a writing signed by both oarties"? an/dor no waiver of any right will be a continuing waiver"?
If there are any of these clauses, then your oral arrangement won't be binding on the parties.
See a landlord/tenant lawyer for help.
PLEASE READ THIS BEFORE YOU COMMENT, EMAIL ME OR PHONE ME. I'm only licensed in CA. This answer doesn't make me your lawyer, and neither do follow-up comments and/or emails and/or phone calls, and you shouldn't expect me to respond to your further questions if you haven't hired me. We need an actual agreement confirmed in writing before any attorney-client relationship is formed. This answer doesn't constitute legal advice, and shouldn't be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.