Certified GKH Gardening Expert
Other than removing by hand, the best way to remove invasive thyme is using herbicides. Choose a broadleaf herbicide, since these will kill the thyme but not the grass. See this article to learn about what is available:
Organic alternatives are discussed in this article:
Some other strategies for removing invasive plants are discussed here:
Thyme is in the mint family, so the advice should apply to it as well.