Kim,
Your screenshot "Document preview of Screenshot 2024-04-24 1527472.jpeg" seems to show that the desired cutting of the triangles is completely unrelated to the text, so you can just lock the text and work with the triangles.
I agree with pixxxelschubser that the triangles look as if they are made with Brushes, quite likely as open paths.
Simple cuts with the Scissorst Tool as suggested by Monika is the obvious and straightforward way, but in case of Brushes, this will fundamentally change the shapes/thickness variations.
In case of Brushes, you can use an Opacity Mask or similar (with the right combination of Clip and Invert Mask options), or a Clipping Mask, in order to hide the unwanted parts and obtain the desrired rounded appearance at the ends with both triangles have a common rounding. That could consist of a Mask that includes the two desired roundings, and either covers the unwanted parts using Opacity Mask with Clip unticked or similar, or covers the desired parts of the triangles using Clipping Mask or Opacity Mask with Clip ticked.
But in case of Brushes, and especially since you mention erasing/cutting, I believe the most straightforward/manageable solution to get the simplest artwork would be to:
1) Lock the text;
2) Expand the Brushes (Object>Expand Appearance); this will give you a Group which holds all the Brushed parts, no need to Ungroup it;
3) Create a circle for each end that has the desired rounding and cut away the part that extends into the desired part of the Brushes, but leaves (at least) the part that forms the desired as the cutting path;
4) For each (remaining) cuttung path from 3), Object>Path>Divide Objects Below;
5) After deselecting everything, and then use the Direct Selection Tool to select and delete all the Brushed paths between the cuts; you can press Alt/Option to select whole paths within the Group, and you can go on selecting and deleting until everything is gone.
This ought to give you a Group of only the desired simple paths.
In 5) while selecting/deleting part of 4) you can temporarily hide the text to ensure that there is nothing behind it.
The remaining parts of the circles thatform the cutting paths in 3) are exactly the same paths that would form part of the construction of the Masks, whether Opacity or Clipping.
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