Sounds more like a bad constant velocity (CV) joint (clicking sound). Check the joint on the passenger side--they normally go first. Look for a split boot and grease slung all over the place. If this is the case, you will likely need to install a new or remanufactured "half axle."
Test: In a large parking lot, turn your steering wheel all the way to the right, shift into reverse, and then start going backwards in a small circle. The noise should be even more pronounced, if it's a constant velocity joint problem.
Remember to change your transaxle fluid every 30,000 miles, when it's hot. I recommend you use Amsoil Synthetic 5W-30 Synchromesh Manual Transmission Fluid (MTF). It normally takes slightly less than 2 quarts.
I believe it's a CV joint problem and not a transmission problem, because I've never known someone to have a problem with their Civic manual transmission. They are extremely reliable, even after 150,000 miles. That's why most people in the world buy Hondas with manual transmissions. The U.S. is the main market for automatics. They are torque goblers and I would never buy a small car with an ATX.
Reading the link below may help you have trouble-free driving experience with your Civic:
https://www.askmehelpdesk.com/cars-t...tml#post219991