Remove triangles from Delaunay triangulation without altering connectivity list

Essentially, I want to go from something that looks like this:

to something that looks like this (pardon the paint):

Where the red lines are constraints. There are several ways of indexing/removing triangles posted on other questions, but all of them end up changing the data type from "nx3 delaunayTriangulation" to "(n-#trianglesremoved)x3 double". Consequently triplot appears to disregard the constraints and connects everything into a big mess.

Attempting to modify the original triangulation using "dt.ConnectivityList=newList" "triplot(dt)" produces an error saying "Cannot assign values to the triangulation".

Does anyone know how to remove triangles while preserving the data type?

[KSSV]

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