"...Is the Olpymics mentioned in the Koran? It predates the Koran by a long time, so is there any ban on competing for women?..."

Women wearing skimpy clothes and being treated as object of lust and pleasure is present now and was also present then during the period of ignorance before the advent of islam.

Islam eradiacted these bad practices by commanding hijab to preserve modesty of women. If women can participate while maintaining the standards of modesty set by islam then they are free to do so.