Unless the author used code that was never really valid C++ (even for 2003), you should be ok as far as compiling and building the library. If you do run into any compilation errors, it should be a minor fix to get rid of the errors.
However, one thing you may encounter (hopefully you won't) is that the program may give different results, have bugs, etc.
If this is the case, this would usually mean that the author used C++ that may be valid syntactically, but either produces undefined behavior or other scenario that is not desirable. If this occurs, you would need to debug the code to see where it goes wrong. Many times, a newer compiler/linker will produce an executable that exposes an undiscovered / hidden bug that was always lurking in the program.
Another possible but more rare scenario is where the programmer is using valid C++ syntax that has well-defined behavior for C++03, but behaves differently for C++11 or C++14. The link in the comments by @ShafikYaghmour discusses this.