For whatever reason, when I put the first equation in the question box it renders correctly (in the preview) on the math Stack Exchange site, but wrong on the physics Stack Exchange site (PSE). The opposite is true for the second equation.
When I right-click on the second equation in the preview and select "Show Math As TeX Commands", it shows me the LaTeX code of the first equation. I think this is some kind of bug. I'm mainly posting this as I'm wondering what it'll look like in the actual post.
$$Γ{}_{\mu} T_{\kappa}{}^{\lambda }$$
$$Γ{}\_{\mu} T\_{\kappa}{}\^{\lambda }$$
Edit: Ok, that's just weird. So now that it's posted, the top equation looks right, but the bottom one is all messed up? Why? The bad thing about this is new questions need to be made to test this out (maybe answers would work too?). It looks the same in edit mode as it does when posted. How odd...
Edit 2: Simplified the example. Also, the glitch doesn't manifest when posting an answer, only question creation. My browser is Google Chrome/Version 107.0.5304.88 (Official Build) (64-bit) and my operating system is Windows 10, 21H2.