Moto disc brake calipers don't move. They hold the brake pads which clamp onto and retract from the brake disc by being moved by the hydraulic action of the pistons upon them that slides them along the pins (blue lines). Even with all the gravel road riding my moto experiences, my pad assemblies are not out of alignment like your example. Maybe the perspective of the photo is skewing things.
The pads should be stabilized in their positions by the spring (red line). The three pins (blue lines) should be parallel. The center pin creates the spring tension. There is a shallow channel in the center of each pin into which the spring should engage. In your image the spring appears cocked off center, not engaged in the center pin channel and the center pin also appears out of alignment with the other pins. The loop at one end of the spring appears disengaged in its channel located in the center of the
lower pin in the image. The spring should be centered over the disc (yellow line) and equidistant from the inside walls of the caliper; it appears cocked within the caliper instead.
What is acting on these parts to move them out of position? Were they ever installed correctly? Is it an optical illusion? The whole assembly needs inspection and cleaning. The pads can be removed without removing either the caliper or the wheel. You might clean the crud off the assembly, to the extent possible. You could use a screwdriver blade to attempt moving the spring into alignment on the pins first. That might ease disassembly. You'll need a drift of suitable length to drive out the two long pins, starting at the hooked end of the spring. Do it slowly and prevent the spring from rebounding. Next, pivot the spring to remove the center pin, then remove the pin from the looped end of the spring. Poke the pads from their positions.
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