There are 2 points about this sentence :

1. About tenses

Here, we are talking about an event (implied by the use of the “passé composé“). You meet someone once, then you know him/her. So here, you refer to the moment you met him, not about the fact you know him at the present.
To use depuis, which continues in the present, you would have to change the tense, and so use present, in order to say you are still in touch with him :

Tammy connait Tex depuis sa 3ème année de Fac à Lyon.

We would say “Tammy connaissait Tex depuis…” if we mean Tammy doesn’t know Tex anymore, or if one of them is gone.

2. About the moment description

To use depuis, you have to talk about a precise moment, implicitly saying it was a short period of time:

Tammy connait Tex depuis sa 3ème année de Fac à Lyon.

Note that saying “depuis ses études” sounds weird… Maybe because of the pronom possessif “ses”. We would better say “depuis la Fac” for instance, which talks about the same period of life.

Whereas pendant is used when you talk about a period, and implicitly saying it lasted a certain time (it was not brieve).

Here, it is not precise enough to be used with depuis.
Note you could use depuis with those kind of elements :

depuis la maternelle, depuis le lycée, depuis qu’on est enfants, depuis la nuit des temps, depuis qu’on a travaillé ensemble…

Conclusion

Tammy a connu Tex pendant ses études à Lyon

is the correct answer.

The ongoing present action would be expressed by using present tense:

Tammy connait Tex depuis ses études à Lyon

This implies she still “knows” him, in the sense they’re still seeing each other now.

In your sentence, this currently going relation isn’t implied… She might have known (actually, met) him during her studies, but it might be they didn’t see each other since then. Note that this formulation (the one from your question) might aswell be used to describe an ongoing relation, the context being there helping to understand if it’s still ongoing or not :

J’ai connu ma femme/mon meilleur ami pendant mes études à Lyon