I've had those exact same problems importing graphics into TLP. It has something to do with the color depth of the imported image; for some ungodly reason, TLP will try to match maybe 2-3 colors out of a 4-color palette and turn the image into a mess. I don't remember exactly how I've fixed it; it can be done, but it's a @#$% to hassle with.
This is one of the myriad reasons why I use Tile Molester. Create a new file, set the bit depth to twice that of the ROM file (i.e. if you're editing a 2BPP NES or GB game, edit the new file in 4BPP), then import the image into the new file. The extra color depth not only guarantees all four colors will be represented, but also gives you leeway to fix the colors to match the intended palette using the color replace tool.