Please note that this tutorial is only meant for Rasbian Jessie, although it might (to some extend) also help with similar issues on other Debian versions. Do this at your own risk (however, the likeliness of a failure is rather small in our opinion).
First step: Download more recent version of dnsmasq compiled for Raspbian Jessie from the official sources
wget https://archive.raspberrypi.org/debian/pool/main/d/dnsmasq/dnsmasq-base_2.76-5+rpi1_armhf.deb wget https://archive.raspberrypi.org/debian/pool/main/d/dnsmasq/dnsmasq_2.76-5+rpi1_all.deb
Second step: Ensure requirements are fulfilled
sudo apt-get install libnetfilter-conntrack3 libmnl0
Third step: Install downloaded packages
sudo dpkg -i dnsmasq-base_2.76-5+rpi1_armhf.deb sudo dpkg -i dnsmasq_2.76-5+rpi1_all.deb
Fourth step: Verify it worked:
Dnsmasq version 2.76 Copyright (c) 2000-2016 Simon Kelley Compile time options: IPv6 GNU-getopt DBus i18n IDN DHCP DHCPv6 no-Lua TFTP conntrack ipset auth DNSSEC loop-detect inotify
You should now be able to use Pi-hole v3.3 on Raspbian Jessie.