I currently code the physician side of Radiation Therapy, and I also used to work in facility reimbursement contracting. So, I can offer a little information and also a little insight.
77300 is a dosimetry calculation. You might also see it documented as a "dose calc." It's the mathematical calculation to determine the radiation dose distribution. In the context of Gamma Knife, it can also be called a shot.
77371 is the facility's charge for the complete course of treatment of Stereotactic Radiosurgery (SRS) in one session. (Gamma Knife is a form of Sterotactic Radiosurgery with a Cobalt-60 machine.)
If this is a Medicare patient, I can tell you that CMS will reimburse a Comprehensive APC (C-APC) payment for 77371. Your 77300 and 77344 don't get reimbursed separately - it is bundled into the C-APC payment for 77371.
If this is a Commercial insurance patient, most facility insurance contracts will typically have a fixed case rate for Gamma Knife services. You should be able to verify that for the specific patient's insurance.
For you as a UR nurse, I can tell you that this claim is probably not worth you spending a lot of time on.
1) It's unlikely that you'd ever get approved to exceed the MUE of 10 for 77300 regardless of what you sent in.
2) Even if you did by some chance get the MUE overturned, it likely wouldn't affect total reimbursement the facility would receive anyhow.
The facility's reimbursement is going to be driven by the 77371 as that case rate or comprehensive APC. Because of that, it likely wouldn't matter if there were 3, 10, or 83 units of 77300 on the claim - it all gets bundled into the comprehensive payment the facility receives for 77371 anyhow.
IMO, I'd issue a corrected claim for the 10 MUE units, so the insurance can pay the 77371. That way it frees your time for denial reviews that actually could bring in additional reimbursement for the facility!
Good luck!
BTW - ASTRO is a great resource if you ever need to look at future radiation therapy claims:
https://www.astro.org/Daily-Practice/Coding