Why is the particle omitted in this relative clause?

Firstly, using the particle が would make no sense at all. が marks the subject of a verb, so 先週がセーターを買いました would mean that "last week bought a jumper". Unless you have some bizarre world where you have anthropomorphised the weeks then this sentence is pure gibberish.

は and が are not interchangeable (see this). は can mark a subject, but it does not do so in this case. The subject in this sentence is the hidden/implied "I".

Adding は to 先週 denotes that either 'last week' is the topic of the sentence, or that you are contrasting last week with some other time see this post.

Finally, you are right that は is not normally allowed in a relative clause, but there is an exception. は can be retained if it is used as a contrast marker rather than as a topic (see this post).

In conclusion, no particle is needed in either the full sentence above or in the sentence which is just the relative clause.