They are merely using the blockchain technology and nothing else. Doesn't mean that it will be in direct competition with bitcoin nor will it affect bitcoin price. Even if they have their own cypto what people are still interested in is the decentralized function. Not having that doesn't sound like crypto in the first place.
Would they even need their own coin? Couldn't they just tweak the blockchain tech and use it without it? The coins are just a reward to incentivize miners but banks will surely just use their own computers and their incentive is the money they will save using this system. A bank mining their own coin would be pointless in my opinion and essentially worthless.