You have accepted Hircine's challenge and followed the will of the Father of Manbeasts. Now, you are the Champion Of Hircine, and the Hunting Grounds of the the Sport of Daedra are waiting for you, if you will choose so.
Joining the Companions, you find that to join the Circle, where you were invited by Skjor, you need to participate in a blood ritual.

About the Lore of the Circle: "Kyrnil Long-Nose, a legendary Harbinger, from the Second Era, began the tradition of trusted advisors called the "Circle". It was named after Ysgramor's Circle of Captains. Its purpose was to serve as an example to the younger, newer Companions.
Over time the purpose of the Circle was somewhat subverted and it evolved to become a group where all members were secretly werewolves.
Based on Kodlak's Journal, a previous Harbinger called Terrfyg was the one responsible for introducing the Companions to Lycanthropy. Terrfyg originally made a pact with the Glenmoril Witches that stated if the Companions hunted in the name of their lord, Hircine, they would be granted great power. They had not believed the change to be permanent, but the Companions were deceived.".

The purpose of the Circle was subverted. By the original Lore you don't need to be a werewolf to be in a Circle. But, now, you need to persuade the Skjor, who is in favor of Hircine's gift.

- I am the Champion of Hircine, Skjor.
- What? Is this true?
- Yes. By this, I ask to become a member of the Circle without a blood ritual.
- This is unexpected, new blood. If a Hircine himself recognized you as a Great Hunter... Yes, you can be a member of the Circle. I will not contradict the great Father. You will be a great addition to our Circle, Champion of Hircine. We shall celebrate tonight. There's a pack of werewolf hunters camped nearby, at Gallows Rock. We will take them down. Aela will escort you.

Q: Does this mod changes the original quest's options?
A: No, this mod adds an additional option. But, it changes some dialogues with the Aela the Huntress.
Q: I don't see the additional option.
A: You need to be the Champion Of Hircine (finish the Ill Met By Moonlight Quest).
Q: On arrival at Gallows Rock, character's hands are invisible in first-person-view. Why?
A: This happens because of the scripted scene and engine render limitations. Simple re-equipment of weapon or spell for each hand solves this in seconds.
Q: Will my character be a true non-werewolf with this mod?
A: Yes. A true non-werewolf, clean from the Daedric curse, who does not have werewolf abilities, immunity and any racial relations to werewolves. Will also be clean from the deep background script (global Companions script) relations, script event, that being independent from The Silver Hand Quest, added the "beast blood" just for joining the Circle, disregarding the "blood" and abilities of the character (bool Property PlayerHasBeastBlood = false auto conditional ; gets set true when you join). Now, as your character will be absolutely clean from any werewolf relations, including deep scripted, when joining the Circle, you can sleep and feel fully rested, as a non-werewolf Champion of Hircine member of the Circle.
Q: There is a conflict of the script (TIF__02000D65) with Better College Application (Plugin Version) mod's script with the same name, why?
A: This happens due to the Creation Kit's default naming system. The scripts are different, but created through the Creation Kit. This conflict is not critical, just place Better College Application mod after this mod in your load order when you will be applying to enter the College, and then place it before this mod. I, personally, use the No-Plugin Version, which is fully compatible.
Q: Compatibility with Enhanced Skyrim Factions - The Companions Guild?
A: Compatible with "Requirements Only" version.
Q: Is there a way still, to become a werewolf, even with this mod?
A: Interestingly, yes. Known thanks to user, pedantic, who found the way to do so. As Dawnguard add-on provides a one-time opportunity to restore your lycanthropy by speaking to Aela, and, since I did not touch this particular dialogue option, you will have the option to gain "the gift of beast blood", if you will ask Aela about this.