Ignore the dirt, but the piece my finger is on.
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That piece sits between the bedsides under the tailgate. If you look at yours, it's as wide/long as your tailgate is, whereas on mine (stepside) it's only as wide as the stepside tailgate.
To make it work you have 3 options.
1. Get some snips or anything that'll cut it, and trim it down to as wide as the strip on the stepside bumper (I'll go measure the piece for ya if you want, or
2 get a stepside bumper, or
3. Replace the step pad on top of your bumper with one from a stepside.
I'd just trim it unless you just need a new bumper. Also the filler neck is rubber if I remember correctly, and it's clamped together, so you "should" be able to trim it down to the length needed for the stepside bed. (I'm not sure how much you'd need to trim it.)