It is not wrongful to admit to a crime committed by the Plaintiff in a complaint
There is no prohibition on making allegations in a complaint that admit to criminal conduct by a plaintiff. Sometimes the criminal conduct is related to the relief sought in a manner that will make available the defense of "unclean hands", but often it will not.
For example, the common law rule is that a trespasser may recover in tort for personal injuries or deaths suffered on land when the owner of the land places undisclosed booby traps on the premies that are deadly or cause serious injury. This is true, at common law, even though trespassing is a crime and even if the trespasser was not just trespassing, but engaged in burglary. I don't know if that is still good law in California, but it illustrates the general principle that admitted to a crime in a complaint, is not per se prohibited if truthful.
Similarly, in a suit alleging a violation of minimum wage laws or worker safety laws, a complaint might acknowledge that the plaintiff was an undocumented alien not allowed to work (which incidentally is a civil offense rather than an actual crime), and that the employer used knowledge of this fact to wrongfully fail to honor the worker's rights.
Similarly, an admission that a purported marriage was invalid and involved statutory rape when entered into, isn't a bar to a claim for alimony or child support or property division in a divorce case, if the marriage subsequently became a legal marriage during a period in which the couple resided in a common law marriage state and met the requirements to have a common law marriage.
A Motion to Strike is a tool that is used when a pleading contains gratuitous irrelevant or scandalous statements about a defendant, not self-incriminating information.
Sanctions are possible for a knowing and bad faith inclusion of factually false statements in a complaint in some circumstances, but usually only near the conclusion of a case or in collateral litigation.
It is commonplace for some facts alleged in a complaint to later be determined to be untrue at trial or earlier in the litigation, and this in and of itself is not sanctionable or improper except that it undermines the ability of the plaintiff to prove a claim upon which relief can be granted. Some facts in a complaint are absolutely necessary to prove (e.g. a car accident actually happened in a personal injury case), while others may not be particularly material to a case (e.g. a misstatement regarding the exact place or location of the accident if jurisdiction and venue are still proper and the date is still within the statute of limitations).
An attorney has an obligation to take due diligence under the circumstances to determine that a complaint is factually accurate, but in most states, "verified complaints" (i.e. complaints whose factually allegations are sworn to be true) are the exception rather than the rule, "verified complaints" are almost never verified by the attorney, and an attorney is entitled to rely on the truth of factual assertions provided by a client absent a reason to know otherwise (and a "verified complaint" sworn to under oath by a client, will often insulate an attorney from allegations of lack of due diligence to investigate the facts).
Typically a defendant will simply deny allegations that the defendant believes are untrue that are contained in a complaint, with all allegations not denied deemed admitted by the defendant.
A general denial is not an appropriate tool to cast doubt on the honesty of an attorney, and is generally only permitted when either every single factual allegation of the complaint is denied, or when the complaint violates the rule requiring facts to be alleged on an itemized and specific basis and instead is vague and narrative in form, making point by point admissions and denials of the complaint impractical.
Indeed, general attacks on the honesty or integrity of the attorney, in general, as opposed to in a particular instance, are almost always improper in the context of a particular lawsuit, or even an ethical complaint against the attorney seeking sanctions related to the attorneys' license to practice law. The legal system is set up so as to very rarely make the outcome of a case hinge on the truthfulness of the lawyer and avoids putting the testimony and truthfulness of the lawyer at issue via several ethical rules and procedural aspects of lawsuits.
A complaint is primarily a statement of the client and not the lawyer. It is only secondarily a statement of the lawyer who certifies that due diligence has been done to determine its factual accuracy and that is a low standard.
If there is evidence that knowingly false allegations were included in the complaint and that the attorney did not exercise due diligence or knew the allegation to be false, that could result in sanctions in a motion filed later on in the case (usually at or close to the dismissal of the case), when the facts and knowledge of the facts have been established (for which the sanction would typically be attorneys' fees unnecessarily incurred by the defendant to defend the suit), and possibly also ethical sanctions against the lawyer (much less common), but that would ordinarily happen only much later in the case.
In some circumstances it is possible to bring a collateral action for malicious prosecution or abuse of process against the attorney and/or client. But, when the alleged wrongdoing arises from the content of the complaint, a showing that the complaint does not state a meritorious cause of action and is also groundless and/or frivolous and/or vexatious is required, not merely a showing that the facts alleged are inaccurate.
Under the "American rule" the default position is that costs of litigation (filing fees, copying costs, expert witness fees, etc.) are recoverable by a prevailing party, but not attorneys' fees or the disruption and lost time and money that the fact of being sued creates in a defendant's life causes, subject to several fairly narrow exceptions. A groundless, frivolous or vexatious lawsuit is typically one of the exceptions to the American rule for attorneys fees (although even then, not to the time and distress caused to the defendant/client).