Modify your tileset, you should put a margin between tiles of 1px and a extrude 1px in your tiles to avoid this problems.
This tile map is from the parkour tutorial and there is no such gridlines while runing with emulator.
Emulator and device has a bit different behavior. Just try it.
Checked a new Tile. Same result. i think i am missing some point 
Here is my tiled map editor settings.
Did you edit the source image too?
Yes source image has 1px margin. Is it possible to provide a sample tilemap which i can test.