Weird Situation - How would you handle it?

Why don't they want you to recruit for next summer? Are they planning to give you offers to come back?

fuck it bro, use it anyways

Unless you signed an NDA where it says you can't publicize it then just put it on ur resume

That is stupid.

Your resume is meant to highlight your work experience and education.

Are you working at this bank? If yes, put on resume. It is that simple, the explanations you provided make absolutely no sense. Major red flags on the bank. Not putting it on your resume is actually being dishonest to the firms you are applying to, I just don’t get it.

I’d say use it anyway. Most of the BBs don’t ask for references or will only confirm employment once you’re hired for the background check. By that time you should be done with your internship and within the period they said you could use it. Doesn’t make sense why they won’t allow you in the first place.

I'm very curious what bank this is but I can understand if you can't tell us. That being said, I echo the above comments, unless it is explicitly included in your contract, do it anyway. But I should note that even if you don't, a lot of recruiters will look at this year as a gap anyway and would understand if you weren't able to get an internship given the pandemic. As long as you network right, you should be fine anyway, especially since you're only a sophomore.