Hello,
I'm sorry to hear you didn't get the BCG offer (but making it to final round is super impressive in any case!)!
GPA will mostly play a part in how likely you are to pass the resume review and get invited to interview. At this stage, GPA is just one of the factors they will be considering, on top of everything else on your resume. So, if you have some good work experience and demonstrate impressive leadership skills, teamwork, and quantitative analysis via your resume, a less-than-perfect GPA will not outweigh all of those things. If you are invited to interview and progress on, GPA will hold even less weight - I highly doubt it had any impact on your outcome with BCG, for instance.
However, at this stage, your GPA at time of application is not something you can change. I know it's easier said than done, but I would try to focus on the things you have control over in your application, and try to make sure they are as good as possible. Spend some time workshopping your resume and cover letter to make sure you portray yourself in the best light. And then go ahead and apply! There are no guarantees of course, however I don't think a 3.53 GPA will necessarily prevent you from getting an interview, if the rest of your application is good (frankly, there's not a huge amount of difference between 3.53 and 3.6, so if you made it to final round with 3.6, it would seem that you had lots of other great things to offer as a candidate!).
So, don't be too demotivated, focus on improving the things you can control, and apply! Best of luck!