The GUDHI library is a C++ library, with a Python interface (via Cython). It is available under a MIT license in order to ease the external contributions. There are still GPLv3 and LGPL dependencies for many modules.
Third-party libraries license
Some of the GUDHI modules depend on third-party libraries that are under a GPLv3 or a LGPL license (CGAL, Miniball, PyKeOps). In the documentation “Copyright: MIT (GPL v3)” in the package list stands for exactly the situation described: GUDHI code is MIT, but there is a dependency on GPL code, so for practical purposes for a user it is as if this package was GPLv3.
If you want to use a GUDHI package identified as “Copyright: MIT (GPL v3)” and GPLv3 does not fit your development requirements, do not hesitate to contact them for a commercial license.
ext/, at the root of the source tree, contains a copy of some third-party libraries for convenience. They are not part of GUDHI and have their own license.