So the issue seems to be with Litmus. The email I tested yesterday was sent from Litmus Builder, and in iOS Mail the various elements are converted to links. The same code pasted into my ESP and sent from there does not display the links. I'd never sent out of Builder, but it appears to connected some how.
Without seeing the rest of your code, I'm just throwing out ideas, but here are three:
1) Add align="center" to your table. that will move it to the center.
2) Wrap your table in another table where the width is set to 100%, and again add the align=center to the existing table.
3) Instead of putting your copy directly in the td, put another table in the td with a smaller width, and center that table with your copy in it. I think you'll want to set the td containing this new table with a width of 100%.
I had the same problem in Eloqua. It didn't recognize the usual flag for tracking a link if buried in the [if mso]. I did find that if I took the link from outside the [if mso], after saving the email so Eloqua added its additional tracking parameters, I could paste that into the [if mso] and Eloqua would then track it.
Rather than just using <td>s for the two areas (icons and links), you want to use two full tables to hold those, and then add the classes so the responsive styles you're using will resize the tables so everything stacks correctly. So starting at your blue row:
table (align left, class=250pxT, holds your icons, includes tr/td)
table (align right, class=250pxT, holds your links, includes tr/td)
This is going to break some of the other parts of your email - you'll need to use some of the classes defined in your styles to adjust the width of the other tables.