The simplicity and seeming insignificance of this error is exactly what makes it fatal.
I’ve come across quite a few reasons that have made admissions committees reject applicants. Some were just not good enough, while others had violated policies. However, the one that I very vividly remember was shared by a Stanford admissions committee member.
This member told a publisher, that the one applicant she hated rejecting was someone who had merely made the careless mistake of not adding a small promotion that she was going to receive after she had submitted her application.
According to the adcom, this applicant was going to get her acceptance letter soon and did not even require that promotion for it. she was a strong candidate and was a favorite amongst the adcoms. But her careless mistake got her a reject from Stanford.
So, while I do suggest you reach out to the admissions committee members and rectify this mistake of yours, make sure to ask them if there is anything else that you can do to make up for it.