Context. The Space-based multi-band astronomical Variable Objects Monitor is a Chinese-French mission dedicated to the study of the transient sky. It is scheduled to start operations in 2024. ECLAIRs is a coded-mask telescope with a large field of view. It is designed to detect and localize gamma-ray bursts in the energy range from 4 keV up to 120 keV. In 2021, the ECLAIRs telescope underwent various calibration campaigns in vacuum test-chambers to evaluate its performance. Between 4 and 8 keV, the counting response of the detection plane shows inhomogeneities between pixels from different production batches. The efficiency inhomogeneity is caused by low-efficiency pixels (LEPs) from one of the two batches, together with high-threshold pixels (HTPs) whose threshold was raised to avoid cross-talk effects. In addition, some unexpected noise was found in the detection plane regions close to the heat pipes.Aims. We study the impact of these inhomogeneities and of the heat-pipe noise at low energies on the ECLAIRs onboard triggers. We propose different strategies in order to mitigate these impacts and to improve the onboard trigger performance.Methods. We analyzed the data from the calibration campaigns and performed simulations with the ground model of the ECLAIRs trigger software in order to design and evaluate the different strategies. Most of the impact of HTPs can be corrected for by excluding HTPs from the trigger processing. To correct for the impact of LEPs, an efficiency correction in the shadowgram seems to be a good solution. An effective solution for the heat-pipe noise is selecting the noisy pixels and ignoring their data in the 4–8 keV band during the data analysis.Results. The trigger threshold is the minimum value of the signal-to-noise ratio that is required to claim that ECLAIRs has detected a candidate event that is not related to a background fluctuation. After introducing the efficiency inhomogeneity in the imaging simulation, the trigger threshold in the 4–8 keV band increased by a factor of 5.75 times and 1.43 times due to the impact of HTPs and LEPs, respectively, in the worst case (on a timescale of about 20 min). The trigger threshold value was restored to its normal value after we applied an efficiency-correction method. Introducing the heat-pipe noise in our simulations in the worst case (timescale of about 20 min) resulted in an increase in the trigger threshold of approximately 100% in the 4–8 keV band compared to observations without heat-pipe noise. Moreover, even with this increased threshold, we estimated a false-trigger rate of 99.26% in the 4–8 keV band and 4.44% in the 4-120 keV band. By accepting a loss of 2.5-5% noisy pixels in the 4–8 keV energy band, we can prevent false triggers caused by heat-pipe noise and reduce the threshold increment to about 20% for the longest timescale (about 20 min) of the ECLAIRs trigger in the 4–8 keV range.