The short answer is, "No". Items, feats, or effects that boost teleport distance do not affect Harrying Step at all.
Blurred Step has the sometimes-annoying combination of both requiring you to be adjacent to the enemy, and only allowing you to shift one square. This often results in you maintaining the same relative position, and not being able to gain any significant tactical advantage aside from adjacency. Also, this generally limits the power's effectiveness to cases where the enemy only shifts one square.
Harrying Step resolves this, by allowing you to shift further than Blurred Step while still maintaining the intent of the power. Now, not only can you follow the enemy however far he shifts, but you are also able to reposition yourself into a nearby space which is more tactically valuable.
Harrying Step specifies a target location relative to another creature, and so is not generally limited to any particular distance. Therefore, it is also not affected by rules which augment teleportation distance. The range of the power may however, depending on wording, be restricted by other effects which inhibit teleportation in the area.
Also keep in mind, when using this feat, that teleportation does carry with it some differences from shifting. For example, teleportation can be used to escape a grab or some immobilizing or restraining effects. There may also be some things which can be triggered by a shift, that would not be triggered by a teleport - or vice-versa. In these cases, and where a Battlemind with Harrying Step wishes to use Blurred Step to move only one square, it will be important to specify whether the movement is a shift or a teleport.
To specifically address the Ring of Retreat, I find the significant terms here to be "increase the distance teleported". With Harrying Step, the maximum "distance teleported" is effectively infinite provided that the destination is adjacent to the target. So, there is no way to increase that. That is, unless you want to get into some really finicky ruling that limits the augmented teleportation to only being used for destination squares on the opposite side of the target.