The title and plot point refers to the zoot suit, a suit with high-waisted, wide-legged, tight-cuffed, pegged trousers, and a long coat with wide lapels and wide padded shoulders. This style of clothing was popularized by Mexican-Americans, African Americans, and Italian Americans during the late 1930s and 1940s.
This is one of the few cartoons where both Tom and Jerry speak.
The radio announcer refers to a 'victory collar' on the suit, which was a nod to wartime fabric rationing.
Zoot suits were fashionable, but also deeply disliked and seen as "unpatriotic", at time of release- which was the height of WW2 rationing. This was because the baggy suits with a long coat violated the fabric rationing regulations of the era. There were numerous instances of violence, and even 1943's famous 'Zoot Suit Riot' (in L.A- the city where Tom and Jerry was produced), instigated by upset over people wearing Zoot Suits.
The ukelele Tim says was popular in another era, so the femme fatale kitty rightly accused him of being 'behind the times' or...a square.