SQL Server MDW - Query for data collector retention period
Inside the database you selected for Management Data Warehouse there is a table called [core].[source_info_internal] that contains a column days_until_expiration

This query gives you the retention periods per collection set:

SELECT [collection_set_uid], [days_until_expiration]
FROM [core].[source_info_internal];


Returns:

+--------------------------------------+-----------------------+
|          collection_set_uid          | days_until_expiration |
+--------------------------------------+-----------------------+
| 2DC02BD6-E230-4C05-8516-4E8C0EF21F95 |                    14 |
| 49268954-4FD4-4EB6-AA04-CD59D9BB5714 |                    14 |
| 3006169E-D33A-4101-A1DE-9F0DABF7D84E |                    30 |
| B83A3832-37CD-4C7A-88F6-6696DA5A7E43 |                    30 |
| 7B191952-8ECF-4E12-AEB2-EF646EF79FEF |                   730 |
+--------------------------------------+-----------------------+


The collection set descriptions are unexpectedly in msdb so if you want the names of the collection set along with the retention period you could use:

SELECT msdb.[name],  mdw.[days_until_expiration]
FROM [core].[source_info_internal]  mdw
INNER JOIN [msdb].[dbo].[syscollector_collection_sets_internal] msdb
on mdw.[collection_set_uid] = msdb.[collection_set_uid];


which returns (on my system):

+---------------------------------+-----------------------+
|              name               | days_until_expiration |
+---------------------------------+-----------------------+
| Disk Usage                      |                   730 |
| Server Activity                 |                    14 |
| Query Statistics                |                    14 |
| Stored Procedure Usage Analysis |                    30 |
| Table Usage Analysis            |                    30 |
+---------------------------------+-----------------------+


Please note however that the Agent job that purges the data calls a stored procedure that accepts parameters so this query lists the default retention periods. If somebody changed it at the job step level you wouldn't get that information.

The procedure definition:

ALTER PROCEDURE [core].[sp_purge_data]
    @retention_days smallint = NULL,
    @instance_name sysname = NULL,
    @collection_set_uid uniqueidentifier = NULL,
    @duration smallint = NULL,
    @delete_batch_size int = 500
AS


So somebody could have overridden the default settings, you could look at the source code for that procedure to follow the entire logic.