If you place a dried inked shirt into a washing machine, then there's a good chance it will come off when exposed to heat. This is why it needs to be cured using an iron. Once this is done, the ink will be set, and you won't have to worry about it.
With ironing, you can either apply direct heat for around 15 seconds or a safer method would be to use baking or brown paper. Iron over this paper for about 90 seconds, giving the t-shirt a break in between that time for a few seconds to make sure it doesn’t burn.