You should only care about that when it does prevent pose a problem
Then you are setting up yourself for a lot of trouble.
Another part of memory management is thinking about ownership (to which the substring discussion is very much related) and it pains me to see how many bugs are caused by code like:
Foo getFoo() {
return myFoo;
}
Where Foo is some mutable class and the invariants of the wrapping class suddenly don't hold anymore because some outside code is mutating the Foo instance through the pointer/reference.Throw in some amount of concurrency and you get something that is not only hard to debug but also difficult to reproduce.
tl;dr: in a GCed language you need to think about memory management and ownership as well.
(Note: I am not arguing against garbage collection.)
That's exactly the point: caring about the actual memory used by interesting may not be as important as other parts of the application, or may not be important at all for now. You should only care about that when it does prevent pose a problem (performance, impossibility to evolve features, ...) (all while making the initial code flexible enough to be potentially changed in the future)