It could be the cervical mucus plug
that is usually discharged just before the onset of a period. Some amount of menstrual disturbance is to be expected during the first few months with birth control pills. It is also possible that she may be going to have her period soon. The possibility of pregnancy
also should be suspected as very early pregnancy can abort as a white piece of tissue only. Please get further suggestions from your consultant. Hope your query has been clarified. Take care.