SET LOCAL <var> doesn't become undefined after transaction is commited

Hi
We are using dynamic settings via SET LOCAL for row level security.
I would like to clarify that I'm seeing the correct behaviour
I create a new session to the database, I run the following query:

SELECT current_setting("session.my_tenant_id");

I will get the following error:
pq: unrecognized configuration parameter \"session.my_tenant_id\"

However, once I run the following transaction
BEGIN READ WRITE
SET LOCAL session.my_tenant_id="f00";
SELECT * FROM someTable;
COMMIT;

Then
SELECT current_setting("session.my_tenant_id");
will return an empty string "". Basically "session.my_tenant_id" becomes
defined.

Is this supposed to work like this or could this be a bug?
Is it possible to entirely undefine "session.my_tenant_id" after the
transaction was committed? Basically I would like to return to the initial
state of the PSQL connection.

Thanks in advance.