Developing low-cost recycled filaments with desirable mechanical properties is a major challenge in the additive manufacturing industry. This research investigated the feasibility of producing 3D-printer filament from recycled high-density polyethylene (HDPE) bottle caps and characterized its shape-memory behavior. Unlike previous studies that neglected the residual stress history from production and spooling, this study demonstrated the inherent error in conventional testing methods by measuring the initial curvature angle and its variation after stress relaxation. The fabricated 1.75 mm filament was subjected to shape-memory bending tests, and the results were compared with those of commercial PLA, ABS, and TPU filaments. The recycled filament, with a shape-recovery ratio of about 80%, behaved similarly to PLA and outperformed ABS. Furthermore, the necessity of a stress-relaxation step in testing protocols was confirmed by observing a non-zero initial angle and unwanted shape recovery after stress relaxation in all samples. The fabricated filament also exhibited a lower density than the other materials, providing a key competitive advantage. Additionally, economic analysis revealed a significant cost reduction compared to commercial counterparts. It is concluded that high-value smart materials do not require expensive resources; recycling bottle caps is presented as an environmentally friendly solution with high application potential, affordability, and significant added value.