Does not reciting the supplication for entering and exiting the bathroom invalidate ghusl al-janabah (ritual bath after major impurity)?

Remembering to say the invocations upon entering and exiting the lavatory is sunnah (recommended), not obligatory. It is recommended to say, "Allahumma inni a'udhu bika min al-khubthi wal-khaba'ith" (O Allah, I seek refuge in You from the male and female evil spirits) upon entering, and "Ghufranaka" (Your forgiveness) upon exiting. Omitting these invocations does not entail sin, nor does it invalidate ghusl or wudu.