Strenuous here means lifting your one rep max, running 20 miles, breaking a personal best sprint time, that sort of thing.
I can attest from personal experience that ice bath right after exercise works in these cases. I’ve even tested it by icing just one leg and not the other. There is a marked difference in recovery by next day.
Ideally you ice the muscles right after workout then put them in a compression clothing so they’re extra warm for the next several hours.