This paper deals with the influence of an incubation medium pH on the hydrolytic degradation of a novel thermosensitive biodegradable triblock copolymer based on hydrophilic poly(ethylene glycol) and hydrophobic copolymer poly(lactic acid-co-glycolic acid) (PLGA-PEG-PLGA), consequently modified at α,ω-ends with itaconic acid (ITA) resulting in α,ω-itaconyl(PLGA-PEG-PLGA). Itaconic acid, obtained from renewable resources, delivers a reactive double bond and carboxylic functional group to the end of PLGA-PEG-PLGA copolymer: this is important for a reaction with biologically active substances. The suitability of the sample degradation was assessed depending on whether the copolymer formed a gel at 37 °C. Two reversible physical sol-gel-sol transitions from a sol (liquid phase) to a gel (solid phase) and back to a sol (suspension) were verified using the tube inverting method. The hydrolytical degradation was evaluated at a physiological temperature (37 °C) in the presence of phosphate solutions, at a pH of either 4.2 or 7.4 by monitoring the decrease of the number average molecular weight of copolymers by GPC. Moreover, the degradation kinetics was confirmed by the HPLC/DAD method, where the increasing amount of final degradation products (lactic and glycolic acids) was detected. The study demonstrated that the carboxylic groups modified copolymer (ITA/PLGA–PEG– PLGA/ITA) is more susceptible to hydrolytical degradation than the unmodified copolymer within first days of degradation at pH 7.4.