The thermal reliefs of my ground polygon to one of the pads of my footprint are just simply weird! I dont know what causes it? It seems to me that the lines leading up from the polygon to the pads are just too thick and are out of proportion to the pad.
You need to change the width of your ground polygon. The polygons are actually made up of many wires drawn to make a continuous surface. If you zoom in on a polygon that is drawn in a non-solid pattern (like an inner layer on a 4 or greater layer board) you can see what I mean.
When you draw the polygon you can choose the size of the wires used, just the same as when drawing wires. You can also change it after the fact using change->width, if I remember correctly.
You probably want to make the width no greater than the width of your IC pads.
This may not apply to you because you use Eagle, but in Altium if you have traces going to pads then you pour a plane over it, it can behave badly. Try removing the (superfluous) traces and repouring it.
Tangentially related: Did you use an auto-router? You might want to adjust your neck-down rules so you actually have a neck, or possibly the trace thickness rules. In any case, because you're using a plane, you should probably do everything manually around those small SMT parts.
