Gregor Samsa works at a job he despises to support his family and he feels they do not appreciate this sacrifice. In fact, he feels it is his duty to support them and there is some honor in that, but he also feels he has no other choice because he has to pay off his parents’ debts. He feels trapped in a life where his only real connection is with his sister. As a traveling salesman, he is moving so much he can never form lasting relationships. So, he is trapped in a situation where all the money he makes goes away – to support his family. No hopes of upward mobility or promotion (his bosses don’t trust any of their employees).
The woman in the fur represents wealth and success. So, for Gregor, it is something to aspire to, but also a tease. The fur is a symbol of wealth. The woman may also represent desire for female companionship; a sex symbol. She could be a symbol of economic and romantic escape.
Gregor’s transformation is a kind of escape from his mundane life, but unfortunately an escape that reinforces his despised position. Likewise, the fur represents wealth and promise, but it is also fur from an animal. So, it could be analogous to his own transformation; the giant insect being attracted to the woman with fur, making her more animalistic, which continues what you might call a perverse fascination with the picture.