Because one project is spraying invasive birdsfoot trefoil does that mean I should too?
How to approach this question for birdsfoot trefoil, or any invasive plant.
First gather information about an assumed invasive plant. Look up websites, talk to managers you know, consult people with a history on the site. For birdsfoot trefoil, Lotus corniculatus, you will likely find experts/botanists/natural areas managers consider it to be invasive. They may not know what to do about it. It has kept me humble.
But should you manage against it at your particular site?
First, study a map of your site that shows where any remnant habitats are located, where the habitat restorations are. Note the good quality from the poor quality sections.
Then map the occurrences of the invasive plant across your site. Below is a 2006 map from Nachusa.
Does the plant occur everywhere? Does it occur on just the very poor restorations, or the old pasture with no native plants? Or is it on the best part of the remnant habitats, or just on the degraded edges of the remnant?
Consider what harm you might do by working against the weed. A quality remnant already saturated with an invasive plant may be a case of leaving the weed alone.
On our Big Jump unit we have birdsfoot trefoil that is very thick and all across the remnant prairie. Decades back trefoil seed was broadcast over that prairie to make a better pasture. To try to spray out the trefoil would leave little else in the way of forbs. Trefoil produces lots of seed that stays in the soil a long time. Trefoil requires decades of annual visits to spray plants. Our resources are limited. So for this unit we want to contain the spread, leave the trefoil on the remnant, and instead spray trefoil in the adjacent ruderal areas. We also spray any trefoil that occurs on our fire breaks or stewardship lanes so we don’t move the seed around on our equipment.
Below: The trefoil in the adjacent fallow field that had about four species of plants: brome grass, timothy, weedy goldenrod, and lots of the yellow trefoil. We used less than 1% Milestone herbicide (1 oz per gallon) as it works on the germinating seeds too. This was not hard to do. We could do this every few years.
On another large unit we have owned a long time we have been carefully backpack spot spraying trefoil from a remnant, and we have been spot spraying in restorations that are adjacent. This effort has been a 27 year long practice with multiple visits every year. A labor of love.
grassland restoration network 
My experience has been that it is best to manage against all non-native plants simultaneously. If only one non-native species is targeted, then another most always takes its place. The question then becomes less of “When to manage against an invasive plant” and more a question of, what is the best use of resources? I would focus on removing all non-native species from the most diverse areas first. These areas have more species to compete with the invasive plants making the results of your work the most lasting. Only after I was able to control invasive species in remnants, high quality restorations, and low-quality restorations would I then put effort into the control of invasive species and the establishment of diverse natives in this heavily invaded fallow field.
When establishing native species, I would particularly focus on plants in the bean and grass families that provide a similar ecological function to bird’s-foot trefoil, brome grass, timothy. I would worry that repeatedly broadcast spraying to kill bird’s-foot trefoil would put the ecosystem in a cycle of repeatedly starting over. This cycle would never allow natives that have a similar ecological function to get established and compete. Broadcast spraying is a strong defense against invasive species. However, progress is only made when diverse natives are established that can provide a good offense.