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It looks right to me for 0.156"/3.96mm header - it should drop in about 1/3 of its length then push home. It should have a cross profile, compare it to a 0.1"/2.54mm which is more like a barb.
Btw that packet below is for 0.1" polarising peg the .156" from RS Stock No. 173-3290 / Mfr. Part No. 15-04-0219