Even people who write their own sophisticated mesh based groundwater modeling codes usually make extensive use of sparse/dense numerical libraries/solvers that are written by linear algebra experts (e.g., UMFPACK/MUMPS/PETSc etc.). The author of these libraries really know their stuff.

So if you are writing your own groundwater modeling code you simply call the above libraries to solve your equations.

Off course 20 years ago when there were no such libraries people had no choice. That is why codes written in 80s and early 90s typically have their own (often poor performing) solver.

Edit: If you're just using a code then don't bother with linear algebra at all. The only thing you need to know is that for large problems you need to use an 'iterative' solver.

If you are interested in computational science aspects of modeling, i.e. the inner workings of the model and how to improve it, understanding linear algebra as well as numerical methods will prove to be very valuable. While it is likely that you will never end up having to implement that matrix inversion or sparse matrix multiply yourself, and instead use one of many well documented production libraries, it is important to understand how they do it and why they do it in a particular way. From my own experience, I can say that most of the time it won't matter, but sooner or later there comes a situation where having knowledge about how low-level operations work will save you from pulling your hair out for weeks.

And this does not go only for linear algebra - I would extend this advice and urge you to strive at also understanding differential equations, discretization, computer architecture, floating-point arithmetic.