The other answers are correct and on the right track, but I will expand on them with the specific mechanism for these mosquitos. The following paper discusses the engineering behind strain OX513A upon which the OX5034 strain is based:
Phuc HK et al. 2007. Late-acting dominant lethal genetic systems and mosquito control. BMC Biol 5:11
Oxitec mosquitos carry a transgenic construct containing two genes. One encodes for a fluorescent marker, DsRed2, for identifying genetically modified mosquitos and the other encodes a protein called tTAV:
The tTAV gene is under the control of a minimal hsp70 promoter flanked immediately upstream by a tetO site. The tTAV protein is a transcriptional activator that binds tetO and enhances expression. What that means in this construct is that expression of the tTAV gene creates more tTAV protein which binds to tetO which leads to more tTAV expression, etc. This is the positive feedback mechanism mentioned in the above image. Importantly, however, the tTAV protein can bind tetracycline and, when complexed, can no longer bind tetO and therefore cannot drive its own expression. In other words, in the presence of tetracycline, there will be minimal tTAV expression.
tTAV overexpression is lethal during development. Although the exact mechanism of lethality isn’t entirely clear, there are some leading hypotheses:
Knudsen KE et al. 2020. Genetic Variation and Potential for Resistance Development to the tTA Overexpression Lethal System in Insects. G3 10(4): 1271–1281
tTA overexpression is thought to cause lethality due to “transcriptional squelching,” that is a general interference in gene expression (Gong et al. 2005). Consistent with this hypothesis, some genes identified by the GWAS were involved in gene silencing (Su(var)2-HP2) (Shaffer et al. 2002; Shaffer et al. 2006), chromatin binding (mamo) (Hira et al. 2013), chromatin remodeling (Hira) (Loppin et al. 2000) and alternative splicing (bru1)(Spletter et al. 2015), which could all influence the level of tTA expression. Other candidate genes were involved in defense response (PGRP-LC, Lmpt)(Jin et al. 2008), the septate junction (cora) (Tepass et al. 2001) and apoptosis (out) (Coffman 2003); all of which are systems that could potentially impact survival. Four genes; eff, tey, CG32085 and CG13085, encode proteins that are predicted to participate in protein ubiquitination and degradation (Thurmond et al. 2018; Gramates et al. 2017). For example, the Eff protein is a E2 ubiquitin-conjugating enzyme (Chen et al. 2009). It has been suggested that overexpression of the tTA protein could cause lethality due to interference with ubiquitin-dependent proteolysis (Gong et al. 2005) as ubiquitination of VP16 is required for activity and also signals destruction (Salghetti et al. 2001).
To summarize, tTAV is a transcriptional activator and, in Oxitec mosquitos, it regulates its own expression in a positive feedback loop: tTAV protein binding to its response element tetO leads to more tTAV gene expression which leads to more tTAV protein. This overexpression of tTAV is lethal during development. However, tTAV can also bind tetracycline and, when it does, it can no longer bind tetO. In the presence of tetracycline, there is no positive feedback loop and and only basal, non-lethal amounts of tTAV are expressed.
Image from the Oxitec website.