Oppose the Petition and make your argument in the opposition.
A motion to strike, even if it were allowed, would be a grand waste of time and effort. An opposition is the place to challenge the legal and factual basis for the claim being made. Make your arguments there.
Opposing a petition to arbitrate can be very complex. Depending on the topic matter of the complaint, different rules will apply. For instance, there are a great many defenses if the complaint relates to employment issues that implicate protective statutes.
If you have not yet procured an attorney, this would be a very good time to do so.
Good luck to you.
This answer should not be construed to create any attorney-client relationship. Such a relationship can be formed only through the mutual execution of an attorney-client agreement. The answer given is based on the extremely limited facts provided and the proper course of action might change significantly with the introduction of other facts. All who read this answer should not rely on the answer to govern their conduct. Please seek the advice of competent counsel after disclosing all facts to that attorney. This answer is intended for California residents only. The answering party is only licensed to practice in the State of California.
A motion to strike would not be available in connection with a petition to compel arbitration.
You can object to the information you feel is irrelevant in connection with your opposition to the petition.
A motion to strike is generally used to reach defects in a pleading which are not subject to demurrer or answer. Hence, a motion to strike does not lie to attack a complaint for insufficiency of allegations to justify relief, as that is a ground of general demurrer.
Code of Civil Procedure section 436 provides the grounds upon which a motion to strike would be appropriate. This includes the ability to strike out any irrelevant, false, or improper matter inserted in any pleading as well as all or any part of any pleading not drawn or filed in conformity with the laws of this state, a court rule, or an order of the court. It also provides that the court may so strike upon motion made or at any time upon its discretion.
So, it appears you could file a motion to strike if it meets the criterion found in the statute. However, as suggested by my colleagues, you could also file an opposition and include a request within the opposition to strike the offending language pursuant to judicial discretion. That would probably be a more efficient way to handle the particular issue.