We don’t often see it described in such detail, and this is a really good story.

Alas, there are still some nitpicks.

…well, the Tiger Lily decided to send someone to make sure everything nothing happens to you guys.
That’s a weird phrase. Would the Guardsman really say this?

... and a faint trail of smoke started to coming off of her wrist.
I believe that "come" would be the correct form here.

Lena studied both men for a moment before putting her hands behind her hand and doing a small twirl.
Where did Lena get a third hand? You probably meant "head".

– we had to throw down a Time Lock to prevent the Daleks from reversing the my unit’s evac—
Choose one.

At the mention of the Vortex Manipulator, Floats Too Low looked up from the its work and nodded.
Choose one again.

You’ve got the remains on one on your hands ...
I guess you meant "of".

HG

THIS IS WHAT I'M TALKING ABOUT! See, all that work paid off! I'm so proud of you. :)

Though now I'm wondering, what are Sigalorians like? And since they're not canon, does this mean Hop is from a fanfic universe?

And she talks an awful lot like William so now I'm wondering if the two are related. Hmmm... *scuttles off to get her conspiracy notebook*

...also, why is she introduced here (as in, on the Board) as Lena Swift when it looks like she's going to go by Hop for the rest of her appearances? Just kind of threw me for a loop when she suddenly changed her name.

Also, not anything wrong with this, but it felt like it took Swift/Hop a very long time to realize the Guardsman is a Time Lord, considering he introduced himself as "of Gallifrey". This could just be me being nitpicky, though.

Also also, a few mistakes I noticed:

The Time Agent’s glanced upwards for a moment.

The apostrophe-S needs to go.

the place seemed to have the life on its own
I think you meant the place seemed to have a life of its own

All in all, an entertaining interlude. :)