Hi Lorraine,

Thank you for your question!   It is a little difficult to identify the plant from the photos because we are in early spring.  Our best guess is it is either Arctostaphylos uva-ursi (bearberry) or Thymus praecox also known as creeping thyme.   It would be helpful if you could send us a clear, close-up photo and a description of the plant (are the leaves hairy or smooth?  what color flower?).   We might have more success in identifying the plant if you wait until it flowers.

Attached below are three articles which show pictures of the plants and it may help you identify which plant you have.  

As far as eliminating the plant, manual removal is time-consuming and physically demanding, but is often quite effective. This can involve mowing, cutting or pruning, digging or hoeing to remove root systems, and disposal of the plant material.  Also, you can try using vinegar as an herbicide. Combine four parts vinegar to one part water. Add about an ounce of dishwashing liquid to a gallon of the mixture. Mix well and pour into a spray bottle. Choose a dry, calm, sunny day and saturate the invasive plant with the vinegar solution.

An even more simple removal method is to pour boiling water on the plants. This works best for young, tender plants and is not as effective for woody-stemmed plants.

Smothering is another organic method. If you have a large area of invasive plants and no "good plants" to save, cover the area with a UV-stable tarp or heavy plastic. This is a slow form of removal and may take up to two years for all of the vegetation to die.

I hope this helps.  Please get back to us with pictures when you can.  Thank you again for your question!

Arctostaphylos uva-ursi - Wikipedia

Arctostaphylos uva-ursi (Bearberry, Bear's grape, Hog Craneberry, Kinnikinnick, Sandberry) | North Carolina Extension Gardener Plant Toolbox (ncsu.edu)

https://www.missouribotanicalgarden.org/PlantFinder/PlantFinderDetails.aspx?taxonid=281446