This is a quotative と, and when used with から like this the difference in meaning is often quite subtle. In this case it's quoting the phrase 「もったいないから」as the justification for 着ない. It's essentially equivalent to saying
However since it's used with と alone (without the 言って or the quotation marks) it's not a direct quote indicating that someone actually said the quoted phrase, but an indirect quote indicating a statement that the person might be thinking or feeling as their justification for not wearing the clothes.
In the end, the resulting meaning is pretty close to what you would get without including the と at all, but the nuance and flow of the sentence feels subtly different. In this sentence, the speaker evidently doesn't fully agree that it is もったいない to wear the expensive clothes, since he's arguing against that line of thought, so it feels more natural to treat the もったいないから as a quoted opinion of the hypothetical owner of the clothes, rather than presenting it as a plain から statement which sort of implies it's a justification the speaker himself is providing.
Also, in this particular case, separating out the もったいないから from the rest of the sentence as a quote makes the sentence easier to parse - it helps to clarify that 高い服を and もったいないから are both separate elements modifying the 着ないでいる, rather than being connected to each other somehow. I'm not sure if 高い服をもったいないから着ないでいる… is strictly ungrammatical, but it sounds like quite an awkward construction that would probably be better avoided (My first instinct would be to replace the を with a が, so that the first two elements are connected, though awkwardly this would change the meaning of the sentence somewhat). The use of the the quotative と makes the existing construction perfectly natural.