Lawyers for the woman claimed the police actions were procedurally unfair and breached her human rights.
She is seeking to judicially review the PSNI over being served with six separate Police Information Notices (PINs) – all since deleted.
The woman at the centre of the challenge has been granted anonymity.
Described as holding strong anti-abortion views, she was involved in “prayer vigils” outside Marie Stopes’ base on Great Victoria Street.
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Pro-life advocates have staged demonstrations and handed out leaflets at the centre which offers sexual and reproductive healthcare and early medical abortions within Northen Ireland’s laws since it opened in October 2012.
Last year high-profile Precious Life campaigner Bernadette Smyth was cleared on appeal of harassing former Marie Stopes clinic director Dawn Purvis.
Charges can only be brought for an alleged course of conduct involving two or more incidents, with PIN notices often featuring.
It was stressed in court that the woman taking legal action has never been convicted or prosecuted for any incidents at the clinic dating back to 2014.
She was accompanied by Mrs Smyth as the challenge got under way.
Her counsel, Fiona Doherty QC, acknowledged the PSNI has been dealing with a highly charged, emotive situation with strong views on both sides.
“Police have to be very careful that their powers and duties are not used by them or exploited by someone else in an attempt to curtail or suppress lawful behaviour by those with opposing views,” she said.
“They must act with scrupulous fairness and must ensure the right of citizens to engage in lawful behaviour is protected.”
Ms Doherty claimed the practice was unlawful in three ways:
• Issuing the PINs to her client was contrary to police policy.
• The notifications were contrary to the rules of procedural fairness and natural justice.
• Police actions were incompatible with the woman’s human rights.
According to the barrister there were inadequate safeguards against the arbitrary service of PINs.
She added: “The retention of information in this case was not in accordance with the law and was disproportionate.”
Even though all six notices issued on her client have been deleted, Ms Doherty argued that the underlying information remains on the police database.
The case continues.