Hey vanlacke,
Open up the texture sample you are having issues with and take a look at the settings applied within.
Texture Settings
Try changing the ‘Texture Group’, the ‘Filter’ applied, as well as the ‘Compression Settings’. All of these will have an effect on the final render of the image in your scene. My first guess would be to set the ‘Texture Group’ to UI and then the ‘Filter’ to ‘Trilinear’ to smooth out the edges. Usually you want to keep the filter at ‘Nearest’ which gives your sprites and a sharp look at the pixel level.
Let me know if you have any other questions.
Cheers,