Seasonale is an oral contraceptive pill containing estrogen. Estrogen passed through milk is not known to have any adverse effect on an infant. However, in some cases, estrogen decreases a woman's milk supply. Progestin-only pills are usually recommended for nursing mothers because they only rarely affect milk supply.
Staining is common both on progestin only pills and on Seasonale. Taking a pill at the same time each day may help, as that may prevent a dip in hormone levels that could lead to bleeding. It may take about two months to adjust to hormonal treatment. Some women stop menstruating altogether on progestin only pills.
If staining on oral contraceptives persists beyond two months, get back to us for guidance. Staining issues are relevant because your staining during lactation should not last forever.
It might prove helpful to read our article ketamim, to review the halachot pertaining to stains.