Do I need to re-zero scope after loosening and retightening mounting hardware?

This post shows just how little I know about guns... As a result of a post I made last week about low light shooting, I purchased a red LED light and installed it onto my scope. I had to loosen the scope mounting hardware to make enough room for the LED light clamp. Now that I have physically moved the mounting hardware, does that mean I need to re-zero the scope? Thanks VERY MUCH in advance!!!
 
I own some Leupold quick disconnect bayonet rings. I can remove and reinstall or swap scopes without POI change. This is the only mounting system I have that doesn't require re zero Without these rings amy mounting change will. require aminor change, especially l if you have a scope stop on the receiver rail.

I really like the bayonet rings because it allows me to remove the scope for air travel. I pack the scope securely in clothing suitcase. I do this because of really bad previous travel experiences. Baggage handlers can be cruel.
 
Thank you so much for all the replies. Info VERY much appreciated! So here's a followup. I have shot at some of the "enemy" (ok , well nutria--night shooting and usually moving critters...). I have missed several fairly close and easy shots--mostly "high" so figured I should re-zero. So.... I <tried> to re-zero the scope tonight as recommended by most here but I think I over-adjusted on the initial tweak and I really don't have any idea where I am now. I'm shooting at an 8" target mounted on a 2' x 2' piece of plywood from about 20 yards out and I hear the pellets hitting the plywood but sometimes i don't even see any entry points. I put some notebook paper on the 2' x 2' plywood so I could see where the pellets are hitting but as noted above but sometimes not even seeing any pellet marks anywhere. I'm thinking I should loosen the scope mounts, reset the right/left and up/down adjustment screws to a neutral points on their adjustment dials, tighten the scope and re-commence attempting to re-zero. I have about 1 1/2 hours invested in this now and I think I'm worse than when I started because of the initial over-adjustments. Very frustrated right now...

Thanks AGAIN in advance.