Okay, here's a newspaper article re. Willah's marriage, and it says she has lived all her life in Decatur County (and if so that is where her birth certificate should be):
Leon Reporter, Leon, Iowa
Thursday, July 3, l924, Leon Journal Reporter
MR. RUEL LESTER BARCUS, of Coleraine, Minn., and MISS WILLAH MINA GIBSON, daughter of MR. and MRS. W. C. GIBSON, of near Garden Grove, Iowa, were united in marriage at the home of A.L. Sears in Center Township, on Tuesday afternoon, July lst, in the presence of the bride's sister and husband, MR. and MRS. DELBERT SMITH, Elder A.L. SEARS performing the ceremony. The bride is well and favorably known, having spent her entire life in this community. The groom is a grandson of MR. SAMUEL HENDRICKS, a former resident of Decatur County, and is engaged in farming. The happy couple will soon leave for their new home in Minnesota, and a host of friends join in congratulations and best wishes for their future success."
An offer to send an original copy of the marriage certificate to any interested family member:
A family tree online says Mathilda Caroline Recter was born 1860 in Mercer County, Missouri; married in Iowa in 1882; lived in Decatur County, Iowa; and died in Tama County, Iowa. No parents given. Seems like your Matilda.
I haven't gotten far enough yet to figure out if this is Matilda in 1880 (maybe you know):
1880 US Census
Princeton, Mercer, Missouri
Albert H. May 45
Martha F. May 38
Clara I. May 14
Agnes C. May 12
Willie H. May 10
Maggie May 7
Laura L. May 5
Fred May 2
Matilda Rector 18, servant, born in Missouri, father born Indiana, mother born Missouri
Finding her with her adoptive parents is not going to help anyway - unless she is noted in the census as Native American. So far the records don't seem to fit with the story that Mathilde was Kiowa but we can't rule it out, especially since she was adopted.