Clearly Littlefinger wrote the ‘pink letter’ in order to set up Jon and his wildling army to fight the Boltons at Winterfell.

When he met with Robyn in episode four, he said “My Lord, come and see,” as he presented Robyn with the gift – the falcon. The pink letter ends on the same words, ‘come and see.’

It was probably on his request that Rickon & Osha got sent to Winterfell as prisoners as well.

His encounter with Sansa in episode five was clearly him planting a few seeds of doubt in her mind, and making her act as he wants – seek out the Tullys in Riverrun.