Based on prior knowledge, we can analyze the relationship between the "month" feature and the task of whether the client subscribes to a term deposit.

Analysis:

- It is possible that certain months might have a higher or lower likelihood of clients subscribing to a term deposit.
- The exact relationship between the "month" feature and the target variable may vary depending on the specific dataset and context.
- It is important to analyze the distribution of the target variable ("yes" or "no") within each category of the "month" feature to determine any potential patterns.

To create the dictionary, we will:

1. Analyze the distribution of the target variable within each category of the "month" feature.
2. Identify the values of each category that have a significant presence of both "yes" and "no" target values.
3. Create a dictionary with the required format, including the relevant values.

Here is the dictionary for the given feature "month":

```json
{
    "no": ["may", "jul", "aug", "nov", "jun"],
    "yes": ["aug", "oct", "mar", "apr", "sep"]
}
```

Please note that the above values are based on general analysis and may vary depending on the specific dataset.