The relevant rule of chatzitza[1] is that something that people normally would remove constitutes a chatzitza that disqualifies the tevilla rabbinically, even if it covers only a minority of the object.[2] In all likelihood, the sticker in question fits into that category. However, your question is more complicated, as we will partially explain.
There are two reasons to suggest that the handle does not need to be tovelled. First, a plastic kli does not require tevilla. Additionally, the handle does not come in contact with the food, and only a kli se’uda[3] requires tevilla. On the latter point, the Shulchan Aruch[4] rules that handles need to be immersed. However, there are different possible ways to explain this halacha, and these can impact on the conclusion regarding your question.
One possible explanation is that a kli’s handle is a distinct, albeit connected, kli that needs tevilla if made from metal or glass. Although it does not come in contact with food, it is attached to and complements a kli that touches food and thus is considered a kli se’uda. If this is the reason, then your handle, being plastic, does not require tevilla, and the chatzitza is not a problem.
Another possibility is that a handle is a secondary part of the kli. Just as one must tovel in its entirety a kli that is part metal and part plastic, so must he tovel the kli’s handle. Therefore, a chatzitza would be as much a problem on the handle as anywhere else on the kli.
A third possibility is based on the assumption that the handle itself is an entity that does not require tevilla, but nevertheless, if it was not immersed in the mikveh, we would say that the kli itself was not totally surrounded by water, which is a basic requirement of any tevilla.[5] In contrast, if the handle was immersed, even with a chatzitza, the entire kli was encompassed by water. According to this approach, the sticker would not raise a problem. Realize that the main part of the kli, which requires tevilla, is unaffected by the chatzitza; all of it touches the mikveh’s water except the place where the handle is connected to it.
On this third point, there may be a machloket among recent poskim. Consider an appliance that holds and heats up food, where the heating element is housed separately from but connected to the part that holds the food. Rav Moshe Feinstein[6] rules that one need immerse only the whole part of the appliance (probably upside down) that hold the food, leaving the electrical section protruding from the water. The Minchat Yitzchak[7] argues, saying that this is not considered immersing the kli.
Rav Feinstein’s ruling is apparently incompatible with the third possibility above, which assumes that a handle is a separate, albeit connected, appendage. If he did, then according to his approach that appendages do not have to be submerged when the main part of the kli is immersed in the mikveh, the Shulchan Aruch would not have required handles to be immersed.[8] The Minchat Yitzchak, however, can accept the third approach.[9]
The Darchei Teshuva[10] addresses your case explicitly and requires removing the chatzitza before tevilla. Several contemporary works accept this opinion,[11] and we found no one who argues. This is apparently in line with the second approach, namely, that the handle is like any other part of the kli. In truth, the Beit Yosef’s[12] explanation for the need to tovel handles seems to concur. Although he does not discuss the case of a plastic-equivalent handle, it is likely that he would agree with the Darchei Teshuva. Thus, although one could make the argument that a chatzitza on a plastic handle is not a problem, the consensus is that another tevilla is needed after removing the sticker.