The Graded Autocatalysis Replication Domain (GARD) model describes an origin of life scenario which involves non-covalent compositional assemblies, made of monomeric mutually catalytic molecules. GARD constitutes an alternative to informational biopolymers as a mechanism of primordial inheritance. In the present work, we examined the effect of mutations, one of the most fundamental mechanisms for evolution, in the context of the networks of mutual interaction within GARD prebiotic assemblies. We performed a systematic analysis analogous to single and double gene deletions within GARD. While most deletions have only a small effect on both growth rate and molecular composition of the assemblies, ~10% of the deletions caused lethality, or sometimes showed enhanced fitness. Analysis of 14 different network properties on 2,000 different GARD networks indicated that lethality usually takes place when the deleted node has a high molecular count, or when it is a catalyst for such node. A correlation was also found between lethality and node degree centrality, similar to what is seen in real biological networks. Addressing double knockout mutations, our results demonstrate the occurrence of both synthetic lethality and extragenic suppression within GARD networks, and convey an attempt to correlate synthetic lethality to network node-pair properties. The analyses presented help establish GARD as a workable alternative prebiotic scenario, suggesting that life may have begun with large molecular networks of low fidelity, that later underwent evolutionary compaction and fidelity augmentation.