The old woman stared at the guest rudely.

Literal

Old-woman [topic-は] guest [object-を] staringly looked.

じろじろ is a 擬態語 for staring in a rude or overly curious manner — eyes examining someone up and down. 御客 (おきゃく) uses the honorific 御. The contrast between the polite term for the guest and the rude staring adds social tension.