Because of their high spatial resolution over extended lengths, distributed fiber optic sensors (DFOS) enable us to monitor a wide range of structural effects and offer great potential for diverse structural health monitoring (SHM) applications. However, even under controlled conditions, the useful signal in distributed strain sensing (DSS) data can be concealed by different types of measurement principle-related disturbances: strain reading anomalies (SRAs), dropouts, and noise. These disturbances can render the extraction of information for SHM difficult or even impossible. Hence, cleaning the raw measurement data in a pre-processing stage is key for successful subsequent data evaluation and damage detection on engineering structures. To improve the capabilities of pre-processing procedures tailored to DSS data, characteristics and common remediation approaches for SRAs, dropouts, and noise are discussed. Four advanced pre-processing algorithms (geometric threshold method (GTM), outlier-specific correction procedure (OSCP), sliding modified z-score (SMZS), and the cluster filter) are presented. An artificial but realistic benchmark data set simulating different measurement scenarios is used to discuss the features of these algorithms. A flexible and modular pre-processing workflow is implemented and made available with the algorithms. Dedicated algorithms should be used to detect and remove SRAs. GTM, OSCP, and SMZS show promising results, and the sliding average is inappropriate for this purpose. The preservation of crack-induced strain peaks’ tips is imperative for reliable crack monitoring.