Hi @Erwan,
This depends on the question you want to answer from your data. Usually we include the factors we are interested or concerned in the model. You need to use your domain knowledge to decide which factors may affect your treatment effects and include them in the model.
Usually it's good to include interaction terms in the model when you have more than one factor in your model. If you know for sure that Collection_month does not interact with Treatment, you can just use the formula “Collection_month + Treatment” . Otherwise, you probably should include the interaction term, using the formula "Collection_month * Treatment". If the interaction term is significant, it means your Treatment effect is depend on the Collection_month. An example would be that your Treatment effect is stronger in Collection_month A than Collection_month B.
You can read this blog post regarding the interaction term in regression models.