How do you know that the 'insoluble particles' contain your ester? Did you analyse them? And how?
Is TEA.HCl completely soluble in DMF at any concentration?
If the particles don't contain your product, but you really don't want to see them, you may try a more lipophylic amine (Bu3N, iPr2EtN...) or one of those very strong amines like N,N,N',N'-tetramethylguanidine, DBU...
If, on the contrary, the particles do contain your product, then it probably means that it's (partially)precipitating as the HCl salt, and in this case you really need a stronger base as the ones cited above, or a different solvent.