The pictured plants are too young to identify with certainty, as they don't have enough distinctive features. (Flowers are key to confirming plant ID, but sometimes the leaf and stem traits on older plants are distinctive enough to get close to a reliable ID.)

Removing any unwanted plant at this stage, regardless of its exact ID, should be fairly easy if they are still seedlings, as they should uproot readily with a hoe, shovel, or other weeding tool. Use of an herbicide is not needed, but if manual removal is too daunting or not feasible, a contact-type herbicide should be all that's needed. Contact herbicides only kill the foliage the spray contacts, whereas a systemic herbicide is absorbed by foliage and moves into the roots to kill the plant. Very young plants like seedlings rarely grow back from the loss of all of their leaves, and a contact herbicide spray will likely be all you'd need (one or possibly two applications, giving the first spray time to work). If you decide to try that approach, find a broadleaf herbicide labeled for home use and follow its directions carefully.

If the plants are a type of Persicaria, those plants tend to prefer soils that stay damp or which are poorly-drained or compacted (since compaction slows drainage when the soil is wet). While we have not had nearly enough rain lately to keep soils that wet, if this is a lower-lying part of the yard or if it's getting runoff from a roof downspout outlet or some other water source (leaky faucet, etc.), that might explain why they're taking over that spot, so fixing the drainage issue in that case should help avoid the problem recurring in the future.

Miri