Unplanted tank is growing plants.

[Naidisbo]

So, I admittedly hadn't been cleaning the gravel in my 10 gallon tank for about a week, as the hose is broken.
It had no living plants as I know nothing about caring for them... However.
Somehow they got into the tank anyway!
There's two sprouts I've seen so far, growing from the base of two different fake plants.
I guess my question is - How do I take care of these little volunteers?
Also, the eels have never been in a planted tank, even at the shop. I know having plants in the tank changes the water chemistry and that eels are sensitive to these changes, so should I just uproot the plants to avoid them getting sick?

<---- Best I could draw as I currently don't have a camera that can get a clear shot.

I don't really know how they even got in there.
I've cleaned the tank thoroughly since the last time I added snails or shrimp.
Could it have come in with the frozen bloodworms??
Seems unlikely, but I don't think I've introduced anything new to the tank in over a month.

 

[eaglesaquarium]

some plants need just a tiny shard of it to get somewhere to propagate into a new plant under the right conditions. Not sure what that is, but it appears like a cryptocoryne. Personally, I wouldn't do anything different (except for the water changes) than before. If the plant can handle no care, great. If not, if it starts to rot pull it. Healthy plants only affect the water chemistry in a good way and never quickly, so they won't bother your eels. Just watch if they turn south and remove them. I'm guessing these plants won't be fussy.