Neither mxDateTime nor Datejs nor that webservice support "last thursday of the month". The OP wants to know all of the last thursdays of the month for, say, a full year.
mxDateTime supports the operations, but the question must be posed in Python code, not as a string.
The best I could figure is parsedatetime, but that doesn't support "last thursday of the month". It does support:
>>> c.parseDateText("last thursday of april 2001")
(2001, 4, 20, 13, 55, 58, 3, 64, 0)
>>> c.parseDateText("last thursday of may 2001")
(2001, 5, 20, 13, 56, 3, 3, 64, 0)
>>> c.parseDateText("last thursday of may 2010")
(2010, 5, 20, 13, 56, 7, 3, 64, 0)
>>>
(Note that neither DateJS nor that web service support this syntax.)
EDIT: Umm, okay, but while the year and the month are right, the day isn't. The last thursday of april 2001 was the 27th. I think you're going to have to roll your own solution here.
It does not support:
>>> c.parseDateText("last thursday of 2010")
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "parsedatetime/parsedatetime.py", line 411, in parseDateText
mth = self.ptc.MonthOffsets[mth]
KeyError
>>>
So one possibility is text substitution: normalize the string to lowercase, single spaces, etc. then do a string substitution of "the month" for each of the months you're interested in. You'll likely have to tweak any solution you find. For example, in some old code of Skip Montanaro which he wrote for an online music calendering system:
# someone keeps submitting dates with september spelled wrong...
'septmber':9,
Or you write your own parser on top of mxDateTime, using all of the above links as references.