Would I have neither advantage nor disadvantage when attacking a grappled creature when opting to restrain via the Grappler feat?

The Grappler Feat states:

You’ve developed the Skills necessary to hold your own in close-quarters Grappling. You gain the following benefits:

You have advantage on Attack rolls against a creature you are Grappling.

You can use your action to try to pin a creature Grappled by you. To do so, make another grapple check. If you succeed, you and the creature are both Restrained until the grapple ends.

The Restrained Condition states:

A restrained creature’s speed becomes 0, and it can’t benefit from any bonus to its speed.

Attack rolls against the creature have advantage, and the creature’s Attack rolls have disadvantage.

The creature has disadvantage on Dexterity Saving Throws.

If on the first turn I grapple a creature, I have advantage on attacks to the creature. On the second turn, I use my action to pin the creature and now we are both restrained.

On subsequent rounds, would I now have neither advantage nor disadvantage when attacking the creature?