If you are talking about places such as zoos and aquariums. Even if they still took animals from the wild on a regular basis like they used to (no longer done) there would not be enough of an impact.
HOWEVER the illegal wildlife trade makes a huge impact. Be it those animals used as "pets" or just for parts. It has caused major problems over the years. Parrot populations in Central and South America have been destroyed because of this.
Of course most species forced onto the endangered species list due to the illegal trade have not had a huge impact on the environment. But there are still issues that pop up. For example nearly all bird species are also pollinators. Be it through their waste, carrying pollen on their body, dispersing seeds, etc... thus less birds, less plants. Life altering? Probably not, but it is still there.
What happens to the environment when certain animals are captured? And do you have a data analysis as an evidence? Thank you!
