Based on prior knowledge, we can analyze the relationship between the feature "month" and the target variable "Does this client subscribe to a term deposit?"

One way to analyze the relationship is by looking at the distribution of the target variable across different months. We can calculate the percentage of clients who subscribed to a term deposit (target = yes) and the percentage of clients who did not subscribe to a term deposit (target = no) for each month.

Here is the analysis and the resulting dictionary:

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

From the analysis, we can see that the months of "mar, apr, sep" have a higher percentage of clients who subscribed to a term deposit compared to the other months. On the other hand, the months of "may, jun, jul, aug" have a higher percentage of clients who did not subscribe to a term deposit.

Note: The values in the dictionary represent the months that have a higher proportion of clients belonging to each target class. For example, if the target class "no" has a higher proportion in multiple months, those months are included in the list of "no" values. The same goes for the "yes" values.