Stopping an area from being engraved

I am trying to design an engraving of a cow with a brand on its rear. I am unable to keep the brand from being overwritten on the engraving. This engraving will be laser etched on a Yeti tumbler cup. How can I stop this from happening?

I’m not sure what are you trying to do, but guessing that exported art covers some specific location where branding is.
With very little understanding of your situation I would try to suggest to use back plotter and manually prune/edit out g-code lines that overwriting branding.

First - export your work to NC. Then back-plot:
You may find stand alone back-plotter or use one very nice online: https://ncviewer.com/
Click graphical elements that are interfering, see corresponding code, remove it and click PLOT to update view.

When happy - save the text.
To run G-code in LightBurn - use “run g-code” next to file open (I think, something like that, I’m not sure exactly).

If these are two images, I don’t know how to proceed.
If the brand is a vector image the Mask tool might be an answer for you.

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