We do not make offerings to the eikon(ai) ,but to the person(s)which represent.
It's acceptble to offer foods,pecuniae,jewelries,and any other precious materials before the eikon(ai).
The practise of pouring red wine over the grave is extreme ancient .It can be considered as a real offering(not like the food which we bring to the tomb always be consumed at a later time).Yes,it's pre-christian,and is still an important part of sinic confucian rite(澆奠、奠酒、獻爵禮）,but at least in the christian east such doing is well accepted(the ban of this practice in Mediolanum was unwonted).
Till today,as far as I know,in Makedonia,Thrake,Skopia,many place of Serbia and Bulgaria,when priest read trisagion over the grave,people offer red wine ,and then priest pour it over the tomb in cross-form.
Other liturgical relic of this practise(pour wine over the tomb of Holy Martyrs)is kept in the service of consecration of an Agia Trapeza.The archiereys pours wine over it since it's tomb of martyr(s).
And it's customary in China to bring various food(maigre only)for paraklesis,parastas,panichis,mnimosino,trisagion(even in the case of a reader service),such food be called"供品/供养/供物”——prosfora/offerings.No one thinks it's a problematic or doubtful practise dagmatically.