My problem with Walmart shopping is that they keep their prices low in part by buying from companies who are paying slave wages in 3rd world countries, and in part by paying their own employees such low wages that many are on programs like food stamps. Walmart even runs food donation programs so that customers can buy food from the store and then donate it to the company employee donation bin! So you're paying one way or another - through your taxes or at the register!
I also have problems with the causes that Walmart and Target corporate owners support. So I don't spend money there just on principle.
I don't sell Mary Kay, but they are a good company that is a member of the Direct Selling Association (that only allows ethical companies into membership) and you are supporting a small business owner. You'll probably find that their products, like Avon (which also does awesome things for women like donating to breast cancer research), also tests ingredients and uses higher quality ingredients.
I think you have to research products that you use near your eyes, and also it matters if you are using waterproof or non-waterproof mascara. A lot of people used to use baby products for things like this, but now that Johnson & Johnson faced a multi-million dollar settlement for causing a death through their baby powder, people are steering away from that stuff too even though one would think it was "mild" and "safe".
I'm saying, there's a trade-off for everything. You might check Consumer Reports to see if they've done a study on cosmetics. Even if it wasn't on eye make-up remover, a good company in some products might be worth considering for other products.