How does Catholicism deal with the apparent paradox/conflict between "love thy neighbour" and "you will be rewarded" I am wondering about an apparent conflict between a call for selfless love topped with a promise of a reward for it. Simply speaking, one is called to behave well (love ones neighbour) out of kindness (certainly not selfishness), but at the same time a reward is promised (those who behave well eventually go to heaven). This seems to entangle selflessless with selfishness in an uncomfortable way. 

The following example hopefully illustrates my concern. Suppose I am encouraging my kid to go help a person in need by appealing to the kid's kindness and compassion. But when done with encouraging, I add "by the way, you will get $10 if you help him/her". This seems to defeat the point of the motivation through kindness and selflessness.

In yet other words, I am concerned that on the one hand there is a morality, an ideal that is attractive for a well-wishing person, but the promise of a reward downgrades this to an act of buying and selling (I do this and then you give me that). 

Worse yet, the  promise of a reward removes the opportunity to choose selflessness over selfishness. There is no longer a choice between behaving selflessly and behaving selfishly because both lead to the same actions in life.
Theologically speaking, through the Holy Spirit we receive the theological virtue of Charity (more commonly called Love), "by which we love God above all things for his own sake, and our neighbor as ourselves for the love of God" (Catechism of the Catholic Church, point 1822). 

Point 733 of the Catechism of the Catholic Church states:


  "God is Love" and love is his first gift, containing all others. "God's love has been poured into our hearts through the Holy Spirit who has been given to us."


Thus, those who are greatly infused with this virtue will by its sole merits express such love through internal and external acts (minding the issue of sin, temptation, selfishness and other obstacles on the way). Again, God is Love, so receiving God through the Holy Spirit (recall the issue of the Trinity) by definition predisposes our will and soul to love! The reward is a non-issue. 

Yet it is true that charity is essential for salvation. Point 837 of the Catechism states:


  ... Even though incorporated into the Church, one who does not however persevere in charity is not saved. He remains indeed in the bosom of the Church, but 'in body' not 'in heart.'


Saint Paul reminds us (1 Cor 13:1-3):


  If I speak in the tongues of men and of angels, but have not love, I am a noisy gong or a clanging cymbal. And if I have prophetic powers, and understand all mysteries and all knowledge, and if I have all faith, so as to remove mountains, but have not love, I am nothing. If I give away all I have, and if I deliver my body to be burned,[a] but have not love, I gain nothing.


Thus, it would have been a bit unfair for Jesus not to let us know that indeed love lead us to heaven. Thus, Jesus is in this sense acknowledging a reality - the means of salvation. He is not suggesting we should love because we would otherwise go to hell. The sole fact that we are made for love is sufficient reason for us to seek the source of this love and make it the aim of our lives.