This appears to be a very aggressive ground cover (Glechoma hederacea) that is often seen trying to take over the garden or lawn. Also known as creeping Charlie, though other more desirable plants also have that common name. From Europe. It should be easy to pull out if it hasn’t gotten too established but once the roots have taken hold, it’s pretty hard to get rid of. Where it can be contained, however, it makes a fine groundcover.
The first thing to understand when working to get rid of creeping charlie is that it, like most lawn weeds, thrive best in an unhealthy lawn. Be sure to use proper mowing, watering and fertilizing practices when caring for your lawn.
Treating your lawn with a broadlead herbicide containing dicamba or triclopyr in the fall and then again in the spring will go a long way towards eradicating this weed. But those herbicides can’t be used in Canada.
There is some disagreement about the effectiveness of borax. If you apply it in the right amount, household borax is slightly more toxic to creeping Charlie than to grass, so you can kill the weed but spare the lawn. It does have its limits: It’s going to burn the grass if you apply it too heavily, and you can apply it only once a year for 2 years before you exceed the level that will harm grass.
To treat an area of approximately one thousand infested square feet, dissolve 10 ounces of Twenty Mule Team Borax in four ounces of warm water. When you have all the borax in solution, mix this into two and a half gallons of warm water, stir well, and spray directly on the weed with a sprayer that has never held chemicals of any kind! (One that you’ve used to apply non-toxic things like deer repellant, compost tea, or beneficial nematodes is fine; just remember to always clean your sprayer after every use, including this one—you don’t want any residual borax in there.)
You’ll get the best results when the weed is dry and rain is not predicted for a few days afterward. And be vigilant when any new runners appear. You need to keep pulling because not every single root will be killed and new plants will germinate from seed. No matter what method you use, you will have to fight over several years.