Does the presence of a very small speck of nail polish after performing ghusl following menstruation invalidate it, and what is the ruling on the prayers of that day?

Nail polish (manicure) must be removed before performing ablution (wudu) or ritual bath (ghusl) if it prevents water from reaching the skin, because it is obligatory to make water encompass the entire body during ghusl, and the nail is a part of the body that must be washed. If it is not removed, the ghusl is incomplete. The opinion of the majority of scholars, which states the obligation of removing any barrier, even if slight, is the most cautious and absolves one of responsibility.

Therefore, the ghusl is not valid if this nail polish remains. You must wash only the affected area and repeat the prayers you performed before removing it. There is no need to repeat the ghusl from the beginning, as continuity (muwalat) is not a condition for ghusl according to the majority of scholars.