NATO and the US do not fund any programs in Georgia. Georgia finances 100% of the programs itself.
According to the “Security Assistance Monitor of the Center for International Policy”, in 2015-2019, the US allocated financial assistance to Georgia in the military field amounted to 167 million US dollars. In 2019 US allocated 35 million US dollars.
The US funds Coalition Readiness Support Programsupporting the participation of Georgian troops in Peacekeeping Mission in Afghanistan - ”Resolute Support Mission”. Military exercises play the most important role in the training of Georgian soldiers and upgrading their qualification. Georgia hosts various military exercises, including “Noble Partner” and “Agile Spirit”, organized by the USA and its partners.
In April 2019, NATO approved the “ Black Sea package ”. The framework of the package envisages training of Georgia’s naval forces and Coast guard service, paying visits to ports and sharing information. In addition, NATO vessels will participate in exercise together with Ukrainian and Georgian vessels. On March 18, 2019, NATO-Georgia exercise started at NATO-Georgia Joint Training and Evaluation Center (JTEC), Krtsanisi National Training Center. Three hundred and fifty soldiers from 21 NATO member states and 3 partner states participate in the exercise. The aim of the exercises held in the framework of Substantial NATO-Georgia Package is to strengthen Georgia’s defense capability. In 2018, Georgia and NATO signed an agreement, based on which the vehicles worth more than a million Euros will be transferred to the NATO-Georgia Joint Training and Evaluation Center (JTEC).
The narrative is part of a larger campaign aiming at influencing public support towards Georgia's NATO aspirations and portray neutrality as the most rational foreign policy choice for Georgia. See here for other examples of disinformation targeting Georgia.
More about the NATO/US military assistance to Georgia can be found here.