The bank will not remove the mold because of liability issues. You might also have some issues with conventional loans closing on a house that has mold too. They will want a inspector to indicate why they think the property has mold and what needs to be done to resolve the mold issue. Then the loan company will want a guaranty that you will address those issues before the closing or right after the closing.
As indicated before a FHA 203k loan might work but need to find a company that will issue it and that may be difficult.
Is this truly active nasty mold (you can usually smell this easily) or is it just old dried out mold that may look more menacing than it is?
Remediating a mold problem is usually not too difficult - well ... sometimes it can be - depending on the root cause. The essence of it are two-fold:
1. Incoming moisture. This is the root cause and needs to be dealt with first. Mold loves a moist environment. Get rid of that, then clean the mold and you are good to go. Sometimes fixing moisture issues is actually pretty simple and not too costly. Sometimes, it's just that the drain spouts just come right down next to the house and don't extend away enough. Sometimes, the ground isn't graded well enough and the water comes back (or combination of this and the former). Is it possible to check out that basement during or right after a big rain? Is there water coming in, where and how much?
2. Get rid of the mold. Can be done yourself pretty cheaply - get a tyvek suit from home depot, a proper mask - about $25-30 that is labeled for use with mold and hazardous substances. Get a mold removal concentrate, some buckets, sponges, a 1 gallon sprayer, some plastic sheeting, etc. You see where this is headed ... there are more details as to how to do it but this is easily found on Google.
3. After getting rid of all the mold. Prep the masonry walls with some type of acid etc or muriatic acid. Then seal it with Dry-Lok or similar.
A mere home inspector is not qualified to advise you on mold issues, unless specifically trained for it (not likely). They usually just put in their report something like, "buyer may wish to hire a mold specialist to assess and advise ...etc).
My home inspector is also a certified engineer, so I get all sorts of wonderful knowledge from him - and he was absolutely phenominal in helping me to deal with the minor moisture issues in my last house. His price to me on the basement assessment was only $350 and it costs me about $400 to do the rest of everything on my own.
Beware of those outfits that will advise you to deal with basement moisture by expensive internal piping and sump pumps - these guys are mostly scammers. The best ways of keeping water out of the basement all start outside your home, not downstairs.
I hope this helps and feel free to ask follow-ups.