Smartphones are now ubiquitous in daily life, requiring the development of accurate methodologies to study their impact on various aspects of human experience. A promising approach to collect mobile log data is to ask participants to donate, in the context of online surveys, the data that is already available to them through features such as iOS Screen Time and Android Digital Wellbeing. This approach grants participants control over the data they share while providing researchers with valuable observational insights into their mobile and app behaviours. However, the active involvement required from participants poses challenges, leading to low compliance rates and potential biases in the final sample of donors. This study investigates whether the method used to collect data donations, and the incentives provided, have an impact on compliance rates, and the subsequent composition of the sample. Specifically, we implemented a 2 x 3 between-subject web survey experiment (N = 872) in a research-led probability-based panel in Switzerland. Participants were randomly asked to capture and share their data through screenshots, video recordings, and by manual imputation (which we call enhanced recall). Results show that, while compliance rates are very low when using screenshots and video recordings as data donation methods, almost two thirds of participants donated their data by manually imputing their log data. The methods also differ in terms of sample composition, with enhanced recall introducing fewer biases. Overall, our study sheds light on maximizing compliance in data donation studies, offering insights for researchers studying mobile and app usage.