Jan Pietersen Van Husum (he never used the name of Staats, though his sons did) did marry a Grietje Jans in 1653. However, if you check New Amsterdam RDC marriages, you will see that she was from Groenigen. Jan's 1st wife, Elsje Pieters, had been killed by Indians in 1652. Grietje Jans died after 23 Jul 1662 when she was a wit. at Brooklyn RDC, p 112, but bef. Jan's 1663 marriage to Elsje Jans, widow of Fredericks Jansen.
Rev. Henricus Seligns, minister of Brooklyn RDC made an accounting of the wedding money he had received aft. 29 Oct 1662 and before 23 Jul 1664, to his successor. Among the names was "Jan Pietersen, Gld 6." This is as close to the date of his third marriage as we can get.
On 15 Nov 1663, Jan sold a lot located near Whitehall St. New Amsterdam to Hans Steyn. In the deed, Jan as grantee is identified as: "Jan Pieterszen of Gowanus, a shipcarpenter, having married the widow of Frederick Jansen [See Valentine, D. T., Manual of the City of New York, 1865, vol. 2, p 705].
The obvious answer is that Frederick Jansen's wife Grietje had died and he married to a woman named Elsje who was his widow.
She can be seen as Elsje Jans in Flatbush records with step-son Jan Fredericks when his sister Altje Fredericz and Jacob Cornelissen bp. their daughter Grietje. She was Elsje Fredericks with step-son Jan Jansen Staats, for Dina, daughter of Jan Fredericks.
I do not know for sure when Frederick Jans died, nor when Grietje died, but his widow was not Grietje, but Elsje, and she married Jan Pieterszen sometime in 1663.