Unless they changed at one point TD bank did not use ChexSystems when opening a bank account so mayube you can try with them.
I wish you the best of luck!
I don't have any experience with Green Dot's other products, but I have their secured credit card for over two months. No unexpected fees, no nothing. Never say never, but so far, so good.
People with no checking account can pay off their balance by going to stores like Walmart and paying cash or swiping their debit card. (There is a small fee involved.) I wanted to make sure that my Green Dot card got its balance immediately, so when I first got it I went to Walmart, showed them the Green Dot card, they swiped it, took my cash, and in about half an hour I had my $200 credit limit on my Green Dot secured Visa.
I always pay quickly after I charge something on Green Dot (rarely do I have much of a balance at all, and I don't think it's ever gotten up to $50 before I paid it down). I pay in full before any interest builds up.
One of my friends (from church, actually! 
) has had trouble with checking accounts. Where he worked they gave him a special debit card where his wages were available. It's not an actual checking account, just some weird "account" where he can get access to his income. If he were to get a Green Dot secured card (he doesn't, but IF) he could probably go to Walmart and give them his special employee debit card and tell them to transfer it to the Green Dot to pay a balance. Or, he could go online to Green Dot's special payment page and send a payment using his employee debit card. (I always pay my Green Dot payments online using my bank account's debit card because there's no fee involved.)
My friend did find a bank that didn't do Chex systems (or whatever you call it). Even Wells Fargo has something called "Opportunity Checking" which sounds like it's one of these special accounts for people with a troubled checking history.