Certified GKH Gardening Expert
I would be afraid to use anything without causing harm to the Dymondia as well. If the problem is not more than hand picking can do then this will be the most effective method. You can try spraying vinegar directly onto the pest plants, but you will want to be very careful not to spray too much onto the lawn.
This plant will usually outcompete pest plants, over time. Some things are still aggressive though. This article will help you with the care of this lawn: https://www.gardeningknowhow.com/ornamental/groundcover/dymondia-groundcover/planting-dymondia.htm