Molecule optimization is a critical task in drug discovery to optimize desired properties of a given molecule through chemical modification. Despite Large Language Models (LLMs) holding the potential to efficiently simulate this task by using natural language to direct the optimization, straightforwardly utilizing shows limited performance. In this work, we facilitate utilizing LLMs in an iterative paradigm by proposing a simple yet highly effective domain feedback provider, namely $\text{Re}^2$DF. In detail, $\text{Re}^2$DF harnesses an external toolkit, RDKit, to handle the molecule hallucination, if the modified molecule is chemically invalid. Otherwise, its desired properties are computed and compared to the original one, establishing reliable domain feedback with correct direction and distance towards the objective, followed by a retrieved example, to explicitly guide the LLM to refine the modified molecule. We conduct experiments across both single- and multi-property objectives with 2 thresholds, where $\text{Re}^2$DF shows significant improvements. Particularly, for 20 single-property objectives, $\text{Re}^2$DF enhances the Hit ratio by 16.95\% and 20.76\% under loose and strict thresholds, respectively. For 32 multi-property objectives, $\text{Re}^2$DF enhances the Hit ratio by 6.04\% and 5.25\%.