The term 'SITTER's Handful' refers to the job of a babysitter, which is often a difficult and challenging task. The crossword solutions for this term are IMP (3 letters) and BRAT (4 letters). IMP stands for 'important person, ' which is a fitting description for a babysitter, who is responsible for the safety and well-being of the children in their care. BRAT stands for 'bad-tempered child, ' which is a common problem that babysitters must deal with.