You have to edit makefiles. I have never edited this part in order to
compile the Fortran interface to UMFPACK.
Now what happens that ifort receives Linux-like arguments and it does
not like it.
This is unlikely. link.exe in Cygwin has nothing to do with linking. It
belongs to the GNU coreutil:
http://www.gnu.org/software/coreutils/manual/html_node/link-invocation.html#link-invocation
If there was a problem with this, then the messages were quite different.