Mabel told Robert Haydon that she felt like some dowdy, decrepit, horribly dingy old fly. She said it to reassure herself and appear detached and witty, and to show that she did not feel in the least out of anything.
Robert Haydon probably replied something to praise her, which Mabel felt was just politeness, and that he was being insincere. Though she was constantly looking for approval from others, she always felt suspicious when someone actually praised her, or said something in her favour. This shows that she has no self-esteem and a very big inferiority complex.