There is a little bit of research going into selective erasure of traumatic memories (targeted at people with severe anxiety disorders such as PTSD) by targeting synaptic plasticity. This has a long timeline on human use but has interesting potential.
Synapse-specific long-term plasticity underlying memory involves the targeting of plasticity-related proteins (PRPs) to activated synapses. If distinct tags and PRPs are used for different forms of plasticity, one could selectively remove distinct forms of memory. Using a stimulation paradigm in which associative long-term facilitation (LTF) occurs at one input and non-associative LTF at another input to the same postsynaptic neuron in an Aplysia sensorimotor preparation, we found that each form of LTF is reversed by inhibiting distinct isoforms of protein kinase M (PKM), putative PRPs, in the postsynaptic neuron. [...] Thus, the activity of distinct PRPs and tags in a postsynaptic neuron contribute to the maintenance of different forms of synaptic plasticity at separate inputs, allowing for selective reversal of synaptic plasticity and providing a cellular basis for developing therapeutic strategies for selectively reversing maladaptive memories.
In the rat cortex, long-term associative memories vanished rapidly after local application of an inhibitor of the protein kinase C isoform, protein kinase M zeta (PKMζ). The effect was observed for at least several weeks after encoding and may be irreversible. In the neocortex, which is assumed to be the repository of multiple types of long-term memory, persistence of memory is thus dependent on ongoing activity of a protein kinase long after that memory is considered to have consolidated into a long-term stable form.
There are also some other chemicals that, when interrupted, hinder memory consolidation and reconsolidation.
We found that oral administration of the β-adrenergic receptor antagonist propranolol before memory reactivation in humans erased the behavioral expression of the fear memory 24 h later and prevented the return of fear.
Memories formed through association with methamphetamine (METH), but not associations with foot shock or food reward, were disrupted by a highly-specific actin cycling inhibitor when infused into the amygdala during the post-consolidation maintenance phase. This selective effect of depolymerization on METH-associated memory was immediate, persistent and did not depend upon retrieval or strength of the association. Inhibition of non-muscle myosin II also resulted in a disruption of METH-associated memory.
By employing an inducible and reversible chemical-genetic technique, we find that transient alphaCaMKII overexpression at the time of recall impairs the retrieval of both newly formed one-hour object recognition memory and fear memories, as well as 1-month-old fear memories
https://doi.org/10.1111/JABR.12031 (meta-analysis that "suggests that disruption of glutamate signaling under reconsolidation parameters is sufficient to erase drug-related memories")
Electroconvulsive therapy has also been used with some success
https://pubmed.ncbi.nlm.nih.gov/25093782/ (removes memories of traumatic car crash, n=1)
Despite accumulating evidence for a reconsolidation process in animals, support in humans, especially for episodic memory, is limited. Using a within-subjects manipulation, we found that a single application of electroconvulsive therapy following memory reactivation in patients with unipolar depression disrupted reactivated, but not non-reactivated, memories for an emotional episode in a time-dependent manner. Our results provide evidence for reconsolidation of emotional episodic memories in humans.
https://www.science.org/doi/10.1126/science.160.3827.554 (the first study that showed some potential for electroconvulsion -> memory erasure, in rats)
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3677482/ (memories reconsolidation can be interrupted by distraction and/or replacing memories with incorrect memories)
Thus, as previously demonstrated in rodents, fear memory suppression resulting from behavioral disruption of reconsolidation is amygdala-dependent also in humans, which supports an evolutionarily conserved memory-update mechanism.
This is not a conclusive list of memory erasure experiments, but it should provide an overview of the some of the methods that are being investigated
Some of these papers have been mentioned above, but I include them here for completeness.