First the disclaimer. I'm not an expert and have only been actively managing ponds for three years. With that said here is my opinion.
They look like GSF to me, but not being familiar with Warmouth I could be wrong. They look like my GSF.
Based on their size, I would say them coming from another BOW would be unlikely unless that high water event was close to your stocking time. If the high water event was more recent it would be more likely for small fish to enter your pond rather than that size unless you had something like six inches of a foot of water entering. Then larger fish would be more possible. It is the little buggers that really move up and down stream in unbelievably shallow water. I had small BG in my back yard this year, left in the grass as the water receded. Based on their size and stocking time, my best guess is they slipped in with your original stocking. 2" fish can be tough to identify for anyone other than an expert and even the experts might have trouble if they have a thousand fish to sort through and get them in the water before they die. My bet is you unknowingly stocked them.
Yes they will compete with your LMB. Because of the large size of their mouth and aggressive nature they will eat a lot of what a LMB of the same size would eat. If LMB is your main or only goal I would cull them. Particularly where they are that big after only a year. If this was three years down the road and your BG and LMB were well established they would be less worrisome. In my non-expert opinion.
You did not say where you are at. From previous threads on the subject of GSF it appears they are more of a problem the further north you go. The reasoning being GSF mostly spawn once a year and BG have multiple spawns. In the north BG might only spawn a couple times where in the south four of more. The high rate of reproduction of the BG simply allow them to out spawn the GSF in the south so the BG eventually win the competition game unless there are specific conditions where the GSF have the advantage over the BG.
Some guys actually like the dreaded GSF and I have actually been stocking a "few" in my main pond. BUT....... my BG are well established.
You can kind of think of the GSF being a LMB that never gets over a pound or two. They essentially have a mouth the same size as a LMB of the same length. So they compete with LMB of that size.
If you like feisty pan fish, and it appears your other fish are doing fine, you might (GASP!) even want to return a few of the best ones to your BOW. But that is pretty much heresy talk so I could get blackballed for saying it.
My other observation with GSF is you will catch a disproportion of them while angling for BG. In other words it is my contention that if you had exactly 100 BG and 100 GSF in a pond all the same size, when you went fishing you would not catch half GSF and half BG but more something like 2 GSF for every one BG. GSF are very aggressive and are readily catch-able. Therefore you may have fewer of them than you think simply because they are easy to catch. Within about a years time I "fished out" the 50 or so HBG (BGxGSF cross)that slipped in accidentally in my original stocking. They were enough more aggressive that after the first year of fishing and removing them I rarely ever caught another. Since then I have actually decided I like the hybrids and have been raising and stocking them (my pond primary goal is a panfish pond though, not LMB centered)
If you do not want more of them, cull them. If you like them and feel the other fish are established so as to not hurt those populations then keep them. If LMB are your only reason for living, the LMB will love them for lunch but your small LMB will have them as direct competition, unlike the BG that have much smaller mouths.
How's that for a non-committal answer for what you should do with them?
