Let's suppose we're talking about some project.
Do you have experience with the technologies related to the project?
Do we need "the" before "technologies"? The project has a limited set of concrete technologies that are used in this project, so it looks like we should use "the".
Do you have experience with the technologies related to the project?
This reads to me as: "Do you know about the specific technologies that are used (or will be used) in this project we are working on."
Do you have experience with technologies related to the project?
"Do you know about technologies that are similar to the tech used in this project."
For example:
Consider you are working on a programming project that uses Python (a common programming language). Saying "Do you have experience with the technologies related to the project?" would ask the person if they know how to program in python. If you omit the you are instead asking if they know of languages similar to python, such as Java.
However, I wouldn't take the above as a hard rule for everyday speech. Either way the sentence is a bit ambiguous because related can mean "applicable to" or "similar to" and the meaning of the sentence depends on which way you take it.
