That is a strap tie and is meant to distribute a load over a distance (usually across boards, joists, studs, etc.) I see it a lot in attics in Florida (ie hurricane straps) but not on floors. Placing one on a seam, such as the long strap, really doesn't distribute a load but it could be one of those "contractor" quick fixes (ie, I only have 2 straps when I need 4 and I'll just put it down quick and nobody will ever be the wiser ... until I'm long gone). The shorter strap actually looks like it may have been cut back as if someone noticed a bulge or tripped on it and decided to "remove it" without realizing it was a strap tie between two sheets of flooring.
Another thing I noticed is that the flooring appears to be OSB. Although OSB and even particle board get used on flooring, I personally don't like the results when either of these get wet. If it's not in a wet area (it appears to be an exterior entrance such as a mud room) and you don't live in a humid area of the country then you'll probably be fine BUT if you spill a lot of liquid on it or it gets damp over time and bulges and buckles then you'll know why (and have to replace that entire section of your floor). I've seen some people seal OSB and particle board flooring and that might be an option too as well as using marine plywood for wet areas.
As to the fix, I'd leave the straps in place and depending on the flooring you're going to use there are a variety of possible solutions. Carpeting, a nice thick padding should work okay. Laminate or hard wood flooring, notch out an area in the padding or wood itself just as deep as the strap is thick. Vinyl flooring, self leveling compound with a lauan plywood (1/8" thick plywood) to provide a clean smooth surface to attach vinyl or laminate). Tile, if it's level enough then your mortar/thin set will cover it as long as you're already level.
Here's where I found the straps in your picture (www.dhcsupplies.com/store/p/3804-ST9-Strap-Tie-1-1/4-X-9.html):