Yes, it is Catmint. It will seed about somewhat but is not generally invasive. It will be happy growing alongside your thyme. I rely on Nepeta to keep weeds at bay between slower to establish perennials when developing large perennial beds. Thyme and Catmint can be used together this way. You can interplant with taller perennials, shrubs and grasses, as well as early bloomers like the poppies and Zizias shown here. Thyme is a more troublesome spreader than catmint because it hugs the ground so well and roots along the way, taking up more and more ground. Than it spreads by seed too! If you can use compatible, taller plants to reclaim some real estate back from the thyme, maybe much of the thyme can be saved and made to work. I'd rather have thyme filling certain sections of a garden than some weeds I can think of. Hit thyme with a bit of fertilizer in spring, prune taller varieties hard once a year and water before intense heat to keep thyme looking good.