Physically associated hydrogels based on strong hydrophobic interactions often have attractive mechanical properties that combine processability with elasticity. However, there is a need to study such interactions and understand their relation to the macroscopic hydrogel properties. Therefore, we use the surfactant sodium dodecyl sulfate (SDS) and urea as reagents that disrupt hydrophobic interactions. The model hydrogel is based on a segmented copolymer between poly(ethylene glycol) (PEG) and hydrophobic dimer fatty acid (DFA). We show that both agents influence viscoelastic properties, dynamics, and relaxation processes of the model hydrogel. In particular, the relaxation time is significantly reduced by urea, as compared to SDS, whereas the surfactant causes a decrease of the modulus of the hydrogel more efficiently. The reversibility of the effects of SDS and urea can be exploited, for instance, by using an injectable sol that solidifies when the SDS or urea diffuses out of the sample. Surfactant-induced processability may be advantageous in future applications of hydrophobically assembled physical hydrogels.