Marsh marigold, or its cousin
The first thing we need to do is to differentiate between marsh marigold (Caltha palustris)and lesser celandine (Ranunculus ficaria). Even though marsh marigold is a native plant, it can have exuberant growth when in the right site. Lesser celandine, though, is a pernicious weed that spreads by seed and by the small, peanut-sized tubers hidden in the root system.
The glossy, bright yellow flowers of both plants can be confused with each other; even their leaves are similar. Distinctive differences are that the flowers of marsh marigold have just 5 golden petals each, whereas those of lesser celandine have quite a few more petals. This site from Wales has excellent images of lesser celandine blossoms which display each blossom’s slightly grayed center: https://www.first-nature.com/flowers/ranunculus-ficaria.php
The document “Control Options for Lesser Celandine” outlines management: (https://www.nwcb.wa.gov/images/weeds/Lesser-Celandine-Control_Whatcom.pdf). Getting rid of celandine is not a once-and-done sort of thing. You’ll need to be persistent for a number of years. A word of caution: Don’t skip a year before the task is complete.
In the above link, the reference to herbicide (weed killer) is rather broad. But it’s worth know that glyphosate (the active ingredient in Roundup and more) is very useful if applied when the plants are at “50 percent bloom.” The risk of using glyphosate, though, is that it kills, or damages, everything it touches. Even so, applications must be repeated over a number of years to get rid of these persistent weeds.